\u03b2 2 5 b c 50 103 The Six Circular Functions and Fundamental Identities 761 In

# Β 2 5 b c 50 103 the six circular functions and

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β 2 . 5 b c 50
10.3 The Six Circular Functions and Fundamental Identities 761 In Exercises 70 - 75 , use Theorem 10.10 to answer the question. Assume that θ is an angle in a right triangle. 70. If θ = 30 and the side opposite θ has length 4, how long is the side adjacent to θ ? 71. If θ = 15 and the hypotenuse has length 10, how long is the side opposite θ ? 72. If θ = 87 and the side adjacent to θ has length 2, how long is the side opposite θ ? 73. If θ = 38 . 2 and the side opposite θ has lengh 14, how long is the hypoteneuse? 74. If θ = 2 . 05 and the hypotenuse has length 3 . 98, how long is the side adjacent to θ ? 75. If θ = 42 and the side adjacent to θ has length 31, how long is the side opposite θ ? 76. A tree standing vertically on level ground casts a 120 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 21 . 4 . Find the height of the tree to the nearest foot. With the help of your classmates, research the term umbra versa and see what it has to do with the shadow in this problem. 77. The broadcast tower for radio station WSAZ (Home of “Algebra in the Morning with Carl and Jeff”) has two enormous flashing red lights on it: one at the very top and one a few feet below the top. From a point 5000 feet away from the base of the tower on level ground the angle of elevation to the top light is 7 . 970 and to the second light is 7 . 125 . Find the distance between the lights to the nearest foot. 78. On page 753 we defined the angle of inclination (also known as the angle of elevation) and in this exercise we introduce a related angle - the angle of depression (also known as the angle of declination). The angle of depression of an object refers to the angle whose initial side is a horizontal line above the object and whose terminal side is the line-of-sight to the object below the horizontal. This is represented schematically below. θ horizontal observer object The angle of depression from the horizontal to the object is θ (a) Show that if the horizontal is above and parallel to level ground then the angle of depression (from observer to object) and the angle of inclination (from object to observer) will be congruent because they are alternate interior angles.
762 Foundations of Trigonometry (b) From a firetower 200 feet above level ground in the Sasquatch National Forest, a ranger spots a fire off in the distance. The angle of depression to the fire is 2 . 5 . How far away from the base of the tower is the fire? (c) The ranger in part 78b sees a Sasquatch running directly from the fire towards the firetower. The ranger takes two sightings. At the first sighting, the angle of depression from the tower to the Sasquatch is 6 . The second sighting, taken just 10 seconds later, gives the the angle of depression as 6 . 5 . How far did the Saquatch travel in those 10 seconds? Round your answer to the nearest foot. How fast is it running in miles per hour? Round your answer to the nearest mile per hour. If the Sasquatch keeps up this
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