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All Textbook Solutions for Trigonometry (MindTap Course List)

47PS For Questions 1 through 4, fill in the blank with an appropriate word or number. To find the area of a triangle given two sides and the angle between them. multiply ______ the product of the ______ by the _______ of the angle beten them.2PS 3PS 4PS 5PS 6PS Find the semi perimeter of triangle ABC. a=3ft,b=4ft,c=5ft 8PS 9PS 10PS 11PS 12PS 13PS 14PS 15PS 16PS 17PS 18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS 28PS Geometry and Area Find the area of a parallelogram if the angle between two of the sides is 120 and the two sides are 15 inches and 12 inches in length.Geometry and Area Find the area of a parallelogram if the two sides measure 24.1 inches and 31.4 inches and the shorter diagonal is 32.4 inches 31PS Ceomctry and Area The area of a triangle is 80 square inches. Find the length of the side included between A=25 and C=110.33PS 34PS 35PS 36PS 37PS 38PS 39PS 40PS 41PS 42PS 43PS 44PS 45PS For Questions 1 through 10, fill in the blank with an appropriate word, number, or expression. A vector is in standard position if the ____ of the vector is placed at the ____ of a rectangular coordinate system.2PS For Questions 1 through 10, fill in the blank with an appropriate word, number, or expression. To add or subtract two vectors in component form, simply add or subtract the corresponding _____.4PS 5PS 6PS 7PS 8PS 9PS 10PS 11PS 12PS 13PS 14PS 15PS 16PS 17PS 18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS 28PS 29PS 30PS 31PS 32PS 33PS 34PS For each vector, find 12V,V, and 4V. V= 3,7 36PS 37PS 38PS 39PS 40PS 41PS 42PS 43PS 44PS 45PS 46PS 47PS 48PS 49PS 50PS 51PS 52PS 53PS 54PS 55PS 56PS 57PS 58PS 59PS 60PS Approximate the magnitude of each vector and the angle , 0360, that the vector makes with the positive x-axis. Round your answers to the nearest tenth. W=i3j 62PS 63PS 64PS 65PS 66PS Force An 8.0-pound weight is lying on a situp bench at the gym. If the bench is inclined at an angle of 15, there are three forces acting on the weight, as shown in Figure 12. Find the magnitude of N and the magnitude of F.68PS Force Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to the other end to form a swing. Tyler sits on the board while his cousin pushes him through an angle of 25.5 and holds him there. If Tyler weighs 95.5 pounds, find the magnitude of the force Kelly must push with horizontally to keep Tyler in static equilibrium. See Figure 13.70PS Force A traffic light weighing 22 pounds is suspended by two wires as shown in Figure 15. Find the magnitude of the tension in wire AB. and the magnitude of the tension in wire AC.Force A tightrope walker is standing still with one foot on the tightrope as shown in Figure 16. If the tightrope walker weighs 125 pounds, find the magnitudes of the tens ion in the rope toward each end of the rope.73PS 74PS 75PS 76PS 1PS 2PS 3PS 4PS 5PS 6PS 7PS 8PS 9PS 10PS 11PS 12PS 13PS 14PS 15PS 16PS 17PS 18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS 28PS Show that each pair of sectors is perpendicular. i+j and ij 30PS 31PS Show that each pair of sectors is perpendicular. 2i+j and i2j 33PS 34PS 35PS In general, show that the vectors V=ai+bj and W=bi+aj are always perpendicular. Assume a and b are not both equal to zero.37PS 38PS 39PS Find the work performed when the given force F is applied to an object, whose resulting motion is represented by the displacement vector d. Assume the force is in pounds and the displacement is measured in feet. F=67i+59j,d=96i28j 41PS 42PS 43PS 44PS 45PS 46PS 47PS 48PS 49PS 50PS 51PS 52PS Which pair of vectors are perpendicular? a. 3i+4j and 8i6j b. 3i+2j and 2i+3j c. i+5j and i5j d. 2i5j and 7i3j 54PS Problems 1 through 10 refer to triangle ABC, which is not necessarily a right triangle. If A=32,B=70, and a=3.8 inches, use the law of sines to find b.2CT 3CT 4CT 5CT 6CT 7CT 8CT 9CT Problems 1 through 10 refer to triangle ABC, which is not necessarily a right triangle. Find two triangles for which A=51, a=6.5 ft. and b=7.9 ft.11CT 12CT 13CT 14CT Angle of Elevation A man standing near a building notices that the angle of elevation to the top of the building is 64. He then walks 240 ft farther away from the building and finds the angle of elevation to the top to be 43. How tall is the building?Geometry The diagonals of a parallelogram are 26.8 meters and 39.4 meters. If they meet at an angle of 134.5, find the length of the shorter side of the parallelogram.Arc Length Suppose Figure 1 is an exaggerated diagram of a plane flying above Earth. When the plane is 4.55 miles above point B, the pilot finds angle A to be 90.8. Assuming that the radius of the earth is 3,960 miles, what is the distance from point A to point B along the circumference of the earth? (Hint: Find angle C first, then use the formula for arc length.)Distance and Bearing A man wandering in the desert walks 3.3 miles in the direction S 44 W. He then turns and walks 2.2 miles in the direction N 55 W At that time, how far is he from his starting point, and what is his bearing from his starting point?Distance Two guy wires from the top of a tent pole are anchored to the ground on each side of the pole by two stakes so that the two stakes and the tent pole lie along the same line. One of the wires is 56 feet long and makes an angle of 47 with the ground. The other wire is 65 feet long and makes an angle of 37 with the ground. How far apart are the stakes that hold the wires to the ground?Ground Speed A plane is headed due east with an airspeed of 345 miles per hour. Its true course, however, is at 95.5 from due north. If the wind currents are a constant 55.0 miles per hour, what are the possibilities for the ground speed of the plane?Height of a Tree To estimate the height of a tree, two people position themselves 25 feet apart. From the first person, the bearing of the tree is N 48 E and the angle of elevation to the top of the tree is 73. If the bearing of the tree from the second person is N 38 W. estimate the height of the tree to the nearest foot.True Course and Speed A plane flying with an airspeed of 325 miles per hour is headed in the direction 87.6. The wind currents are running at a constant 65.4 miles per hour at 262.6. Find the ground speed and true course of the plane.23CT 24CT 25CT 26CT 27CT 28CT Find the value of b so that vectors U=5i+12j and V=4i+bj are perpendicular.30CT 1GP 2GP 3GP 4GP 5GP We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.For Questions 1 through 10, fill in the blank with an appropriate word or number. The number i, called the _________ ______ is defined such that i2=2PS 3PS 4PS 5PS 6PS 7PS 8PS 9PS 10PS 11PS 12PS 13PS For Questions 12 through 14, determine if the statement is true or false. Every complex number is either a real number or an imaginary number.Write each expression in terms of i. 16 16PS 17PS 18PS 19PS 20PS 21PS 22PS Write in terms of i and then simplify. 49 24PS 25PS 26PS 27PS 28PS 29PS 30PS 31PS 32PS 33PS 34PS 35PS 36PS 37PS 38PS 39PS 40PS 41PS 42PS 43PS 44PS 45PS 46PS 47PS 48PS 49PS 50PS Simplify each power of i. i34 52PS Simplify each power of i. i33 54PS 55PS 56PS 57PS 58PS 59PS 60PS 61PS 62PS 63PS 64PS 65PS 66PS 67PS 68PS 69PS 70PS 71PS 72PS 73PS 74PS 75PS 76PS 77PS 78PS 79PS 80PS 81PS 82PS 83PS 84PS 85PS 86PS 87PS 88PS

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