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All Textbook Solutions for Precalculus

29PE 30PE For Exercises, 21-34, verify the identity. cos2xsinxsin2xcosx=cscx4sinx 32PE For Exercises, 21-34, verify the identity. sin4=4cos3sin4sin3cos 34PE 35PE 36PE 37PE For Exercises 39-44, use the half-angle formula to find the exact value. cos4x+sin2x For Exercises 39-44, use the half-angle formula to find the exact value. sin165 For Exercises 39-44, use the half-angle formula to find the exact value. tan78 For Exercises 39-44, use the half-angle formula to find the exact value. cos712 For Exercises 39-44, use the half-angle formula to find the exact value. cos112.5 For Exercises 39-44, use the half-angle formula to find the exact value. tan75 For Exercises 39-44, use the half-angle formula to find the exact value. sin8 Fill the table for in the given quadrant, what do you notice about the signs of sin and tan2 ?What are the advantages to using the formula tan2=1cossin or tan2=sin1+cos as opposed to tan2=1cos2+cos ?For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2 sin=1161,02 For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2 cos=1213,322 For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2 cos=1237,32 For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2 sin=3365,2 For Exercises 51-56, verify the identity. sin22=csccot2csc 52PE 53PE 54PE 55PE 56PE 57PE 58PE 59PE 60PE 61PE 62PE 63PE 64PE 65PE 66PE 67PE 68PE 69PE 70PE For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first power. b. Graph the result over one period. y=4cos2x4sin2x 72PE For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first power. b. Graph the result over one period. y=6sin2x For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first power. b. Graph the result over one period. y=4cos2x 75PE For Exercises 75-80, find the exact value. cos12arcsin38 77PE 78PE 79PE For Exercises 75-80, find the exact value. tan12cos11517 81PE Find an algebraic expression representing sin2cos1x for 0x1 .A feeding trough for cattle is made from a metal sheet 3 ft wide. The sides of the trough are made by folding up a flap 1 ft wide from each end of the strip. Each flap makes an angle with the horizontal. a. Write an expression representing the area of a cross section of the trough in terms of . b. show that the area can be written as A=12sin2+sin .Consider the triangular area of the roof truss. a. Write the area as a function of sin2 and cos2 . b. Write the area as a function of sin .Consider an object launched from an initial height h0 with an initial velocity v0 at an angle from the horizontal. The path of the object is given by y=g2v02cos2x2+tanx=h0 where x (in ft) is the horizontal distance from the launching point y (in ft) is the height above ground level, and g is the acceleration due to gravity g=32ft/sec2or9.8m/sec2 . Show that the horizontal distance traveled by a soccer ball kicked from ground level with velocity v0 at angle is x=v02sin2g.Refer to Exercise 85. Suppose that you kick a soccer ball from ground level with an initial velocity of 80 ft/sec. a. Can you make the ball travel 200 horizontal feet? b. Determine the smallest positive angle at which the ball can be kicked to make it travel 100 ft downfield to a teammate.Write cos3x as a third-degree polynomial in cosx .Write cos4x as a fourth-degree polynomial incosx .89PE 90PE 91PE 92PE 93PE 94PE 95PE 96PE 97PE 98PE 99PE 100PE Write the product as a sum or difference. a. cos6xsin2x b. cos4xcos5x Use a product-to-sum formula to find the exact value of sin165cos75 .3SP Use a sum-to-product formula to find the exact value of sin75sin15 .5SP 1PE 2PE 3PE For Exercises 3-10, write the product as a sum or difference. sin2sin4 For Exercises 3-10, write the product as a sum or difference. cos3tcos7t For Exercises 3-10, write the product as a sum or difference. cosx2cos3x2 For Exercises 3-10, write the product as a sum or difference. sinx4cos5x4 For Exercises 3-10, write the product as a sum or difference. sin4cos5 9PE 10PE 11PE In Exercises 11-14, use a product-to-sum formula to find the exact value. sin82.5cos37.5 In Exercises 11-14, use a product-to-sum formula to find the exact value. cos97.5cos37.5 In Exercises 11-14, use a product-to-sum formula to find the exact value. cos2524sin1724 15PE For Exercises 15-18, verify the identities. cosx+ycosxy=cos2xsin2y For Exercises 15-18, verify the identities. 2sin4+x42cos4x+y2=cosy+sinx For Exercises 15-18, verify the identities. 2sin4+xy2cos4+x+y2=cosxsiny 19PE For Exercises 19-22, write each expression as a product. sin3+sin10 21PE For Exercises 19-22, write each expression as a product. cos20xcos14x 23PE 24PE 25PE For Exercises 23-26, use a sum-to-product formula to find the exact value. cos2312+cos512 For Exercises 27-34, verify the identity. cos3xcosxcos3x+cosx=tan2xtanx For Exercises 27-34, verify the identity. cosxcos3xsinx+sin3x=tan2x 29PE 30PE 31PE 32PE 33PE 34PE 35PE 36PE 37PE Derive formula (3) on page 601. sinucosv=12sinu+v+sinuv Derive formula (6) on page 602. cosx+cosy=2cosx+y2cosxy2 40PE 41PE 42PE 43PE 44PE 45PE 46PE 47PE 48PE In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourier series named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A0+A1cosx+B1sinx+A2cos2x+B2sin2x+A3cos3x+B3sin3x+... where A1,A2,A3,... and B1,B2,B3,... , are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier series) to model a "saw-tooth" wave and a "square" wave. A â€œsaw-tooth" wave is a periodic wave that rises linearly upward and then drops sharply. In music, such waves are generated in digital synthesizers to give high-quality sound without distortion. Given, fx121sinx1+sin2x2+sin3x3+ a. Graph the first three terms of the function on the window 4,4,1 by 1,1.5,0.5 . b. Graph the first five terms of the function on the window 4,4,1 by 1,1.5,0.5 .In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourier series named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A0+A1cosx+B1sinx+A2cos2x+B2sin2x+A3cos3x+B3sin3x+... where A1,A2,A3,... and B1,B2,B3,... , are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier series) to model a "saw-tooth" wave and a "square" wave. A "square" wave is a periodic wave that alternates between two fixed values with equal time spent at each value and with negligible transition time between them. Square waves have practical uses in electronics and music, and because of their rectangular pattern, they are used in timing devices to synchronize circuits. Given, fx=411sinx+13sin3x+15sin5x+ a. Graph the first three terms of the Fourier series on the window 4,4,1 by 2,2,1 . b. Graph the first five terms of the Fourier series on the window 4,4,1 by 2,2,1 .51PE Solvesinx=2sinx a. Over 0,2 . b. Over the set of real numbers.Solve the equation 1+cos3x=0 . a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2 .Solve the equation 1+2cos2=0 . a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2 .Solve the equation cotx4=1 . a. Write the solution Solve set for the general solution. b. Write the solution set on the interval 0,2 .Solve the equation on the interval 0,2 . 2cos2xcosx3=0 Solve the equation on the interval 0,2 . 4cos2x3=0 Solve the equation on the interval 0,2 . cotxcos2x=cotx Solve the equation on the interval 0,2 . csc2x1=cotx Solve the equation on the interval 0,2 . sin3x+sinx=0 Solve the equation on the interval 0,2 . tanx+1=secx Solve the equation on the interval 0,2 . Give the exact solutions in radians and give approximations in degrees rounded to 1 decimal place. a. cosx=0.6 b. tanx=5 Use a graphing utility to solve the equation cos3x=0.6x. Round the solutions to 4 decimal places.How many solutions to the equation cosx=32 exist? How many solutions exist on the interval 0.2 .2PE 3PE Given the equation sinx=0.2, one solution is x=sin10.2. What is the other solution on the interval0.2 ?For Exercises 5-8, determine if the given value is a solution to the equation. 2sinx+32=sinx a.43b.3 6PE For Exercises 5-8, determine if the given value is a solution to the equation. 10cosx2=8cosx a. 74 b. 34 8PE 9PE For Exercises 9-12, solve the equation over the interval 0,2 . a. cos=32 b. cos=32 For Exercises 9-12, solve the equation over the interval 0,2 . a. cot=33 b. cot=33 12PE For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 2sinx+5=6 For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 32+6cosx=0 For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 5secx+10=3secx+14 For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 32cscx3=3 For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 3tanx+1=22+tanx For Exercises 13-18, solve the equation a. Over the interval 0,2. b. Over the set of real numbers. 5cotx+23=2cotx53 For Exercises 19-20, identify the number of solutions to the equation on the interval 0,2 . a. cosx=12 b. cos4x=12 c. cosx2=12 20PE 21PE 22PE For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) 2cos2x=3 For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) 5+sin3x=4 For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) tan3x=3 26PE For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) 2sin21=0 For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) 5cot2=5 29PE For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) cosx+4=12 For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) tanx2+1=0 For Exercises 23-32, solve the equation. a. Write the solution set for the general solution. b. Write the solution set on the interval 0,2. (See Examples 2-4) cotx2+3=0 For Exercises 33-42, solve the equation on the interval 0,2 . tan+1sec2=0 For Exercises 33-42, solve the equation on the interval 0,2 . (cotx1)(2sinx+1)=0 For Exercises 33-42, solve the equation on the interval 0,2 . sec22=0 For Exercises 33-42, solve the equation on the interval 0,2 . 2sin2x1=0 For Exercises 33-42, solve the equation on the interval 0,2 . cos2x+2cosx3=0 For Exercises 33-42, solve the equation on the interval 0,2 . 2csc2x5cscx+2=0 For Exercises 33-42, solve the equation on the interval 0,2 . 2sin2+sin1=0 For Exercises 33-42, solve the equation on the interval 0,2 . 2cos2x+5cosx+2=0 For Exercises 33-42, solve the equation on the interval 0,2 . cosxtan2x=3cosx For Exercises 33-42, solve the equation on the interval 0,2 . 4sin2xcotx3cotx=0 For Exercises 43-56, solve the equation on the interval 0,2 . 6cos2x7sinx1=0 For Exercises 43-56, solve the equation on the interval 0,2 . 2sin2xcosx+1=0 45PE 46PE For Exercises 43-56, solve the equation on the interval 0,2 . 2cotx=cscx For Exercises 43-56, solve the equation on the interval 0,2 . 2tanx+secx=0 49PE For Exercises 43-56, solve the equation on the interval 0,2 . sinsin3=0 For Exercises 43-56, solve the equation on the interval 0,2 . sin3x+sinx=cosx 52PE 53PE For Exercises 43-56, solve the equation on the interval 0,2 . secx+1=tanx 55PE 56PE For Exercises 57-62, solve the equations on the interval. Give the exact solutions in radians and give approximations in degrees rounded to 1 decimal place. cosx=311 For Exercises 57-62, solve the equations on the interval. Give the exact solutions in radians and give approximations in degrees rounded to 1 decimal place. tanx=3 59PE For Exercises 57-62, solve the equations on the interval. Give the exact solutions in radians and give approximations in degrees rounded to 1 decimal place. 6sinx=1 61PE 62PE For Exercises 63-68, use a graphing utility to solve the equation. Round the solutions to 4 decimal places. sinx=1x3 For Exercises 63-68, use a graphing utility to solve the equation. Round the solutions to 4 decimal places. cos2x=x22 For Exercises 63-68, use a graphing utility to solve the equation. Round the solutions to 4 decimal places. cosx=lnx2 66PE For Exercises 63-68, use a graphing utility to solve the equation. Round the solutions to 4 decimal places. 3sinx=0.5x+1 For Exercises 63-68, use a graphing utility to solve the equation. Round the solutions to 4 decimal places. 3cosx=0.5x+1 For Exercises 69-88, solve the equation on the interval 0,2 . sin2x=2sinx 70PE For Exercises 69-88, solve the equation on the interval 0,2 . cos6x5sin3x+2=0 72PE For Exercises 69-88, solve the equation on the interval 0,2 . cos2x3sinx+1=0 For Exercises 69-88, solve the equation on the interval 0,2 . 4sin2x=14cos2x For Exercises 69-88, solve the equation on the interval 0,2 . sin3xsinxcos3x+cosx=1 For Exercises 69-88, solve the equation on the interval 0,2 . cos3x+cosx2cos2x=1 77PE 78PE For Exercises 69-88, solve the equation on the interval 0,2 . sin3=sin2 For Exercises 69-88. solve the equation on the interval 0,2 . tan2tan=1 For Exercises 69-88, solve the equation on the interval 0,2 . 15cos2x7cosx2=0 For Exercises 69-88, solve the equation on the interval 0,2 . 20sin2x7sinx3=0 For Exercises 69-88, solve the equation on the interval 0,2 . 16cos2x8cosx1=0 For Exercises 69-88, solve the equation on the interval 0,2 . 16sin2x12sinx+1=0 85PE 86PE For Exercises 69-88, solve the equation on the interval 0,2 . sincosx=0 For Exercises 69-88, solve the equation on the interval 0,2 . cos(sinx)=0 The height ht (in feet) of the seat of a child's swing above ground level is given by h(t)=1.1cos23t+3.1 Where t is the time in seconds after the swing is set in motion. a. Find the maximum and minimum height of the swing. b. When is the first time after t=0 that the swing is at a height of 3 ft? Round to 1 decimal place. c. When is the second time after t=0 that the swing is at a height of 3 ft? Round to 1 decimal place A vertical spring is attached to the ceiling. The height h of a block attached to the spring relative to ground level is given by ht=0.8103t+5.8 where t is the time in seconds and ht is in feet? a. Find the maximum and minimum height of the block. b. When is the first time after t=0 that the block is at a height of 6 ft? Round to 3 decimal places. c. When is the second time after t=0 that the block is at a height of 6 ft? Round to 3 decimal places.The monthly sales of winter coats follow a periodic cycle with sales peaking late in the year and before the winter holidays. The monthly sales total Sin$1000 is given by st=350cos6t+6+500 where t is the month number t=1correspondstoJanuary. a. Write the range of this function in interval notation. b. During which months 0t12 are sales at their maximum? c. During which months 0t12 are sales at their minimum? d. In which months, between 1 and 12 inclusive, are the sales $675,000 ?With each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called the systolic pressure and the minimum blood pressure is called the diastolic pressure. When a doctor records an individualâ€™s blood pressure such as "120 over 80,â€� it is understood as "systolic over diastolic." Suppose that the blood pressure for a certain individual is approximated by pt=90+20sin140t where p is the blood pressure in mmHg (millimeters of mercury) and t is the time in minutes after recording begins. a. Find the period of the function and interpret the results. b. Find the maximum and minimum values and interpret this as a blood pressure reading, c Find the times at which the blood pressure is at its maximum.The refractive index n of a substance is a dimensionless measure of how much light bends (refracts) when passing from one medium to another. n=cv where c is the speed of light in a vacuum (a constant) and v is the speed of light in the medium. For example, the refractive index of diamond is 2.42 which means that light travels 2.42 times as fast in a vacuum as it does in a diamond. Snell's law is an equation that relates the indices of refraction of two different mediums to the angle of incidence 1 and angle of refraction 2 . Angles 1 and 2 are measured from a line perpendicular to the boundary between the two mediums. Use this relationship and the table of refraction indices to complete Exercises 93-94. n1sin1,=n2sin2 Assume that a beam of light travels from air into water. a. If the incidence angle 1 is 40 , what is the angle of refraction 2 ? Round to the nearest tenth of a degree. b. Alina attempts to spear a lobster from her boat, if she aims her spear directly at the lobster, will she hit it? Explain your answer.The refractive index n of a substance is a dimensionless measure of how much light bends (refracts) when passing from one medium to another. n=cv where c is the speed of light in a vacuum (a constant) and v is the speed of light in the medium. For example, the refractive index of diamond is 2.42 which means that light travels 2.42 times as fast in a vacuum as it does in a diamond. Snell's law is an equation that relates the indices of refraction of two different mediums to the angle of incidence 1 and angle of refraction 2 . Angles 1 and 2 are measured from a line perpendicular to the boundary between the two mediums. Use this relationship and the table of refraction indices to complete Exercises 93-94. n1sin1,=n2sin2 If a beam of light traveling through air enters a sapphire at an angle of incidence of 23 , what is the angle of refraction? Round to the nearest tenth of a degree.Explain why cos2xcosx12=0 has no solution.Explain why x=sin10.4 is not a solution to the equation sinx=0.4 on the interval 0,2 ?What is the difference between the general solution to a trigonometric equation and the solution over the interval 0,2 ?Explain two different methods to solve the equation sin3x+x=1 by using a graphing utility.For Exercises 99-112, solve the equation on the interval 0,2 . 3tan2x2tanx3=0 100PE 101PE For Exercises 99-112, solve the equation on the interval 0,2 . tan2xsecx2tan2x3secx+6=0 103PE 104PE 105PE For Exercises 99-112, solve the equation on the interval 0,2 . 6sec3x7sec2x11secx+2=0 107PE 108PE 109PE For Exercises 99-112, solve the equation on the interval 0,2 . 32cos1x+1=2 111PE 112PE Consider the equation sinx+1=cosx from Example 10. a. Write the equation in the form sinxcosx=1 . Then write the equation with the left side of the equation in the form ksin(x+) . b. Solve the equation over the interval 0,2 using the form from part (a).For Exercises 114-116, use the technique from Exercise 113 to solve the equation over the interval 0,2 . 3sinx+cosx=1 115PE 116PE 117PE From Exercise 83 in Section 5.3, the cross-sectional area of a feeding trough in the figure is given by A=12sin2+sin . In calculus, you will learn that to find the value of to maximize the area, we need to solve the equation cos2+cos=0 for 02 . a. Find the value of to maximize the area. b. Find the maximum area. c. If the trough is 20 ft long, what is the maximum volume that it can hold?Consider an isosceles triangle with two sides of length x and angle included between them. We have already shown that the area of the triangle is given byA=12x2sin If an isosceles triangle has two 6-in. sides, what angle is required to make the area 10in.2 ? Give the exact value and approximate to the nearest one-hundredth of a degree.For Exercises 120-121, consider a projectile launched from ground level at an angle of elevation with an initial velocity v0 . The maximum horizontal range is given by xmax=v02sin2g , where g is the acceleration due to gravity g=32ft/sec2org=9.8m/sec2 . If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48 m down the field? Assume that the ball reaches the teammate at ground level on the fly. Round to the nearest tenth of a degree For Exercises 120-121, consider a projectile launched from ground level at an angle of elevation with an initial velocity v0 . The maximum horizontal range is given by xmax=v02sin2g , where g is the acceleration due to gravity g=32ft/sec2org=9.8m/sec2 . A quarterback throws a football with an initial velocity of 62 ft/sec to a receiver 40 yd (120 ft) down the field. At what angle could the ball be released so that it hits the receiver's hands at the same height that it left the quarterback's hand? Round to the nearest tenth of a degree.Suppose that a rectangle is bounded by the x-axis and the graph of y=cosx . a. Write a function that represents the area Ax of the rectangle for. 0x2 b. Complete the table. a. Graph the function from part (a) on the viewing window: 0,2,6 by 3,3,1 and approximate the values of x for which the area is 1 square unit Round to 2 decimal places. b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of x for which 2cosx2xsinx=0 . Confirm this result by graphing y=2cosx2xsinx and the function from part (a) on the same viewing window. What do you notice?For Exercises 1-6, prove the identity in part (a), and solve the equation in part (b) on the interval 0,2 . a. Prove that sin4xcos4x=cos2x . b. Solve sin4xcos4x=1 2PRE 3PRE 4PRE 5PRE 6PRE 7PRE a. Compute cos12 by applying a sum or difference formula for cosine. b. Use the result of part (a) to find sin24 and cos24 .For Exercises 1-4, solve the right triangle for the unknown sides and angles. Round values to 1 decimal place if necessary. B=37,a=17 2RE For Exercises 1-4, solve the right triangle for the unknown sides and angles. Round values to 1 decimal place if necessary. b=12.6,c=40.8 For Exercises 1-4, solve the right triangle for the unknown sides and angles. Round values to 1 decimal place if necessary. a=427,b=120 A 20-ft-tall light post casts a 25-ft shadow along level ground. What is the angle of elevation of the sun at that time? Round to the nearest degree.A passenger lift runs 680ft up the side of a mountain from the base to an exit station If the change in elevation of the lift from the bottom to the top of the mountain is 228ft , what is the angle of incline to the nearest degree?A 75-ft guy wire is attached to the top of a tower. If the guy wire makes an angle of 38.2 with the ground, how tall is the tower? Round to the nearest tenth of a foot.A 125-ft kite string is anchored to the ground. If the string makes an angle of 49 with the ground, what is the distance from the anchor site to a point directly beneath the kite? Round to the nearest foot.9RE 10RE A plane flies due west for 2hr then due south for 1hr at an average speed of 375mph . To the nearest degree, what bearing should the plane take for the return trip?A boat travels 3mi east then 7mi south. To the nearest tenth of a degree, what is the bearing from its starting point?A ship leaves a dock on a bearing of S48.2W . After traveling for 1.6hr at 28mph , how far south and west has the ship traveled? Round to the nearest tenth of a mile.A plane flying 275mph on a bearing of N73.5W travels for 4hr . How far north and west has the plane traveled? Round to the nearest mile.For Exercises 15-20, solve ABC subject to the given conditions. Round the lengths of sides and measures of the angles (in degrees) to 1 decimal place if necessary. B=63,a=26,b=42 16RE For Exercises 15-20, solve ABC subject to the given conditions. Round the lengths of sides and measures of the angles (in degrees) to 1 decimal place if necessary. A=26,a=8,b=10 18RE 19RE 20RE For Exercises 21-22, find the area of a triangle with the given measurements. Round to 1 decimal place. A=129,b=14.8mi,c=24mi 22RE Points on a straight shoreline, A and B , are separated by 700yd . Observers at each point record the bearing to a ship at sea. The observer at point A locates the ship at N50E , while the observer at point B notes the ship on a bearing of 50W . If point A is due west of point 8, how far is the ship from each observer? Round to the nearest yard.Two landing points, A and B , lie on the straight bank of a river and are separated by 45ft . Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if ABC is 68 and BAC is 73 . Round to the nearest foot A ranger station at a point R in a wilderness area is located 5.6mi from a campground at point C (see figure). A camper hikes 4mi in a linear path away from the campground to point H , and then shoots a flare straight up as a distress signal. The signal is seen from the ranger station such that HRC=35 . To the nearest tenth of a mile, how far is the camper from the ranger station?Standing on top of a 30-ft lifeguard tower, an observer measures the angle of elevation of a parasail to be 18 . The same observer standing on the ground next to the tower measures the angle of elevation as 21 . If the eye level of the observer is 5ft , determine the height of the parasail to the nearest foot.PointsA,B, and P are collinear points along a hillside.A blimp located at point Q is directly overhead point . Points A and B are 200yd apart, and the angle of elevation (relative to the horizontal) from B to the blimp is 48 . The angle of elevation from point A farther down the hill to the blimp is 44 . a. To the nearest yard, approximate the distance between point A and the blimp and the distance between point B and the blimp. b. Find the exact height of the blimp relative to ground level (distance between P and Q ). c. Approximate the height from part (b).A surveyor fixes a baseline of 64 ft between two points A and B on a plot of land. a. Write an expression for the exact length of AD . b. Approximate AD to the nearest tenth of a foot.For Exercises 29-32, solve ABC subject to the given conditions if possible. Round the lengths of the sides and measures of the angles (in degrees) to 1 decimal place if necessary. a=42,b=66,c=31 30RE

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