CHAPTER 8 Trigonometry

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A plane rises from take-off and flies at a fixed angle measuring 9 with the horizontal ground (Fig. 8-17). When it has gained 400 ft in altitude, find, to the nearest 10 ft, (a) the horizontal distance flown; (b) the distance the plane has actually flown. (8.6) The base angle of an isosceles triangle measures 28 , and each leg has length 45 in (Fig. 8-18). Find, to the nearest inch, (a) the length of the altitude drawn to the base; (b) the length of the base. (8.6)

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Fig. 8-18

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In a triangle, an angle measuring 50 is included between sides of length 12 and 18. Find the length of the altitude to the side of length 12, to the nearest integer. (8.6) Find the lengths of the sides of a rectangle to the nearest inch if a diagonal of length 24 in makes an angle measuring 42 with a side. (8.6) A rhombus has an angle measuring 76 and a long diagonal of length 40 ft. Find the length of the short diagonal to the nearest foot. (8.6) Find the length of the altitude to the base of an isosceles triangle to the nearest yard if its base has length 40 yd and its vertex angle measures 106 . (8.6) A road is inclined uniformly at an angle measuring 6 with the horizontal (Fig. 8-19). After a car is driven 10,000 ft along this road, find, to the nearest 10 ft, the (a) increase in the altitude of the car and driver; (b) horizontal distance that has been driven. (8.7)

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Fig. 8-19

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An airplane travels 15,000 ft through the air at a uniform angle of climb, thereby gaining 1900 ft in altitude. Find its angle of climb. (8.7) Sighting to the top of a monument. William found the angle of elevation to measure 16 (Fig. 8-20). The ground is level, and the transit is 5 ft above the ground. If the monument is 86 ft high, find, to the nearest foot, the distance from William to the foot of the monument. (8.8)

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Fig. 8-20

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Find to the nearest degree the measure of the angle of elevation of the sun when a tree 60 ft high casts a shadow of (a) 10 ft; (b) 60 ft.

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CHAPTER 8 Trigonometry

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At a certain time of day, the angle of elevation of the sun measures 34 . Find, to the nearest foot, the length of the shadow cast by (a) a 15-ft vertical pole; (b) a building 70 ft high. (8.8) A light at C is projected vertically to a cloud at B. An observer at A, 1000 ft horizontally from C, notes the angle of elevation of B. Find the height of the cloud, to the nearest foot, if m A 37 . (8.8) A lighthouse built at sea level is 180 ft high (Fig. 8-21). From its top, the angle of depression of a buoy measures 24 . Find, to the nearest foot, the distance from the buoy to the foot of the lighthouse. (8.8)

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Fig. 8-21

An observer, on top of a hill 300 ft above the level of a lake, sighted two ships directly in line. Find, to the nearest foot, the distance between the boats if the angles of depression noted by the observer measured (a) 20 and 15 ; (b) 35 and 24 ; (c) 9 and 6 . (8.10) In Fig. 8-22, m A 43 , m BDC 54 , m C the result of (a), find the length of AB. 90 , and DC 170 ft. (a) Find the length of BC. (b) Using (8.10)

Fig. 8-22

Fig. 8-23