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All Textbook Solutions for Elementary Geometry for College Students

Prove the statements in Review Exercises 32 to 36 using analytic geometry. The line segments joining the midpoints of consecutive sides of an isosceles trapezoid form a rhombus.Determine whether ABC, with vertices A0,0,0, B1,2,4, and C0,0,8, is an isosceles triangle.38CR 39CR 40CR 1CT 2CT 3CT 4CT Complete the following table of x and y-coordinates of points on the graph of the equation 2x+3y=12. x 0 3 9 y 4 Using the table from Exercise 5, sketch the graph of 2x+3y=12.7CT 8CT 9CT 10CT 11CT 12CT Using as few variables as possible, state the coordinates of each point if DEF is isosceles with DEF is an isosceles triangle with D(,_),E(,_),F(,_).14CT In the figure, we see that mRS-=mVT-=0. Find the equation that relates r,s,andt if it is known that RSTV is a parallelogram. _16CT 17CT 18CT 19CT Use the drawing provided for the proof of the theorem The line segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle. Proof: Given ABC with vertices as shown, let M and n name the midpoints of sides CB- and AB-, respectively. Then 21CT 22CT In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 1 to 6, find sin and sin for the triangle shown.In Exercises 7 to 14, use either Table 11.2 or a calculator to find the sine of the indicated angle to four decimal places. sin90 In Exercises 7 to 14, use either Table 11.2 or a calculator to find the sine of the indicated angle to four decimal places. sin0 9E 10E In Exercises 7 to 14, use either Table 11.2 or a calculator to find the sine of the indicated angle to four decimal places. sin82 12E 13E 14E In Exercises 15 to 20, find the lengths of the sides named by the variables. Use either Table 11.2 or a calculator, and round answer to the nearest tenth of a unit.In Exercises 15 to 20, find the lengths of the sides named by the variables. Use either Table 11.2 or a calculator, and round answer to the nearest tenth of a unit.17E In Exercises 15 to 20, find the lengths of the sides named by the variables. Use either Table 11.2 or a calculator, and round answer to the nearest tenth of a unit.In Exercises 15 to 20, find the lengths of the sides named by the variables. Use either Table 11.2 or a calculator, and round answer to the nearest tenth of a unit.20E In Exercises 21 to 26, find the measures of the angles named to the nearest degree.22E In Exercises 21 to 26, find the measures of the angles named to the nearest degree.24E In Exercises 21 to 26, find the measures of the angles named to the nearest degree.26E In Exercises 27 to 34, use the drawings, where provided, to solve each problem. Angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. The pitch or slope of a roofline is 5 to 12. Find the measure of angle .In Exercises 27 to 34, use the drawings, where provided, to solve each problem. Angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. Zaidah is flying a kite at an angle of elevation of 67 from a point on the ground. If 100ft of kite string is out, how far is the kite above the ground?29E 30E 31E In Exercises 27 to 34, use the drawings, where provided, to solve each problem. Angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. A 12-ft rope secures a rowboat to a pier that is 4ft above the water. Assume that the lower end of the rope is at water level. What is the angle formed by the rope and the water? Assume that the rope is taut.33E In Exercises 27 to 34, use the drawings, where provided, to solve each problem. Angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. An airplane flying at the rate of 350 feet per second begins to climb at an angle of 10. What is the increase in altitude over the next 15 seconds?35E 36E For Exercises 35 to 38, make drawings as needed. In a right circular cone, the slant height is 13cm and the height is 10cm. To the nearest degree, find the measure of the angle that is formed by the radius and slant height.38E 39E In Exercises 1 to 6, find cos and cos.In Exercises 1 to 6, find cos and cos.3E 4E In Exercises 1 to 6, find cos and cos.6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E In Exercise 17 to 22, use either the sine ratio or the cosine ratio to find the length of the indicated sides of the triangle correct to the nearest tenth of a unit.In Exercise 17 to 22, use either the sine ratio or the cosine ratio to find the length of the indicated sides of the triangle correct to the nearest tenth of a unit.19E 20E 21E In Exercise 17 to 22, use either the sine ratio or the cosine ratio to find the length of the indicated sides of the triangle correct to the nearest tenth of a unit.In Exercise 23 to 28, use either the sine ratio or the cosine ratio as needed to find the measure of each indicated angle to the nearest degree.In Exercise 23 to 28, use either the sine ratio or the cosine ratio as needed to find the measure of each indicated angle to the nearest degree.25E 26E 27E 28E 29E 30E 31E 32E In Exercise 29 to 37, angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. Find the length of each apothem in a regular pentagon whose radii measure 10 in. each.34E 35E In Exercise 29 to 37, angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit. In searching for survivors of a boating accident, a helicopter moves horizontally across the ocean at an altitude of 200 ft above the water. If a man clinging to a life raft is seen through an angle of depression of 12, what is the distance from the helicopter to the man in the water?.37E 38E 39E 40E 41E For Exercise 42 and 43, use the drawing and the formula from Exercise 41. Find the area of an isosceles triangle for which s=10.6cm and the measure of the vertex angle is 46.43E 44E 45E In Exercises 1 to 4, find tan and tan for each triangle.In Exercises 1 to 4, find tan and tan for each triangle.In Exercises 1 to 4, find tan and tan for each triangle.4E In Exercises 5 to 10, find the value or expression for each of the six trigonometric ratios of angle . Use the Pythagorean Theorem as needed.In Exercises 5 to 10, find the value or expression for each of the six trigonometric ratios of angle . Use the Pythagorean Theorem as needed.In Exercises 5 to 10, find the value or expression for each of the six trigonometric ratios of angle . Use the Pythagorean Theorem as needed.8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E In Exercises 15 to 20, use the sine, cosine, or tangent ratio to find the lengths of the indicated sides to the nearest tenth of a unit.In Exercises 15 to 20, use the sine, cosine, or tangent ratio to find the lengths of the indicated sides to the nearest tenth of a unit.21E In Exercises 21 to 26, use the sine, cosine, or tangent ratio to find the indicated angle measures to the nearest degree.In Exercises 21 to 26, use the sine, cosine, or tangent ratio to find the indicated angle measures to the nearest degree.24E In Exercises 21 to 26, use the sine, cosine, or tangent ratio to find the indicated angle measures to the nearest degree.26E 27E 28E In Exercises 27 to 32, use a calculator and reciprocal relationships to find each ratio correct to four decimal places. csc 30 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E In Exercises 37 to 43, angle measures should be given to the nearest degree; distance should be given to the nearest tenth of a unit. While a helicopter hovers 1000 ft above the water, its pilot spies a man in a lifeboat through an angle of depression of 28. Along a straight line, a rescue boat can also be seen through an angle depression of 14. How far is the rescue boat from the lifeboat?In Exercises 37 to 43, angle measures should be given to the nearest degree; distance should be given to the nearest tenth of a unit. From atop a 200-ft lookout tower, a fire is spotted due north through an angle of depression of 12. Firefighters located 1000 ft due east of the tower must work their way through heavy foliage to the fire. By their compasses, through what angle measured from the north toward the west must the firefighters travel?44E 45E 46E 47E In Exercises 1 and 2, use the given information to find an expression for the area of ABC. Give the answer in a form such as A=12(3)(4)sin32. See the figure for Exercises 1- 8. a a=5,b=6,and=78 b a=5,b=7,=36and=88 Exercises 1-8 2E 3E In Exercises 3 and 4, state the form of the Law of Sines used to solve the problem. Give the answer in a form such as sin726.3=sin55a a Find if it is known that b=8.1,c=8.4,and=86. b Find c if it is known that a=5.3=40,and=80 Exercises 1-8 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E In Exercises 15 and 16, find the area of the given figure. Give the answer to the nearest tenth of a square unit. Trapezoid 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E In Exercises 29 to 34, use the Law of Sines or the Law of Cosines to solve each problem. Angle measures should be found to the nearest degree and areas and distances to the nearest tenth of a unit. A surveillance aircraft at point C sights an ammunition warehouse at A and enemy head-quarters at B through the angles indicated. If points A and B are 10, 000 m apart, what is the distance from the aircraft to enemy headquarters?32E 33E 34E 35E 36E 37E Show that the form of the Law of Cosines written c2=a2+b22abcos reduces to the Pythagorean Theorem when =90.Explain why the area of the parallelogram shown is given by the formula HINT: You will need to use QN . Exercises 4144 40E 41E 42E 43E 44E In Exercises 1 to 4, state the ratio needed, and use it to find the measure of the indicated line segment to the nearest tenth of a unit.In Exercises 1 to 4, state the ratio needed, and use it to find the measure of the indicated line segment to the nearest tenth of a unit.In Exercises 1 to 4, state the ratio needed, and use it to find the measure of the indicated line segment to the nearest tenth of a unit.4CR In Exercises 5 to 8, state the ratio needed, and use it to find the measure of the indicated angle to the nearest degree.In Exercises 5 to 8, state the ratio needed, and use it to find the measure of the indicated angle to the nearest degree.In Exercises 5 to 8, state the ratio needed, and use it to find the measure of the indicated angle to the nearest degree.In Exercises 5 to 8, state the ratio needed, and use it to find the measure of the indicated angle to the nearest degree.In Exercises 9 to 12, use the Law of Sines or the Law of cosines to find the indicated length of side or angle measure. Angle measures should be found to the nearest degree; distances should be found to the nearest tenth of a unit.10CR In Exercises 9 to 12, use the Law of Sines or the Law of cosines to find the indicated length of side or angle measure. Angle measures should be found to the nearest degree; distances should be found to the nearest tenth of a unit.12CR 13CR 14CR 15CR 16CR 17CR 18CR 19CR 20CR In exercises 21 to 30. Use the drawings. Where provided, to solve each problem. Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit. In the evening, a tree that stands 12 ft tall casts a shadow. If the angle of depression from the top of the tree to the tip of the shadow is 55, what is the length of the shadow?In exercises 21 to 30. Use the drawings. Where provided, to solve each problem. Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit. A rocket is shot into the air at angle of 60 If it is traveling at 200 ft per second, how high in the air is it after 5 seconds? Ignoring gravity, assume that the path of the rocket is a straight line.In exercises 21 to 30. Use the drawings. Where provided, to solve each problem. Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit. A 4-m beam is used to brace a wall. If the bottom of the beam is 3 m from the base of the wall, what is the angle of elevation to the top of the wall?In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit. The basket of a hot-air balloon is 300 ft high. The pilot of the balloon observes a stadium 2200 ft away. What is the measure of the angle of depression?25CR 26CR 27CR 28CR 29CR In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit. An observer in a plane 2500 m high sights two ships below. The angle of depression to one ship is 32 , and the angle of depression to the other ship is 44 . How far apart are the ships?31CR 32CR 33CR 34CR 1CT 2CT 3CT 4CT Using your calculator, find to the nearest degree if sin=0.6691._______Without the calculator, determine which number is larger: a tan 250 or tan 260_________ b cos 470 or cos 480_________7CT 8CT 9CT 10CT 11CT 12CT 13CT 14CT 15CT 16CT 17CT 18CT 19CT 20CT Name the four parts of a mathematical system. HINT: See Section 1.3 2E Which axiom of equality is illustrated in each of the following? a 5 = 5 b If 12=0.5and0.5=50,then12=50. c Because 2 3 = 5, we may replace x 2 3 by x 5. d If 7 = 2x 3, then 2x 3 = 7.4E 5E 6E 7E 8E 9E 10E 11E 12E 13E Nine pegs are evenly spaced on a board so that the distance from each end to a peg equals the distance between any two pegs. If the board is 5 feet long, how far apart are the pegs?The four owners of a shop realize a loss of 240 in February. If the loss is shared equally, what number represents the profit for each owner for that month?Bill works at a weekend convention by selling copies of a book. He receives a 2 commission for each copy sold. If he sells 25 copies on Saturday and 30 copies on Sunday, what is Bills total commission?Use the Distributive Axiom to simplify each expression: a 5(6+7) c 12(7+11) b 4(73) d 5x+3x Use the Distributive Axiom to simplify each expression: a 6(94) c 7y2y b (12)6(4+8) d 16x+8x Simplify each expression: a 6+4 c 16x2y9x2y b 82+32 d 9323 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E In Exercises 1 to 6, simplify by combining similar terms. (2x+3)+(3x+5)2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E

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