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Chapter 8: Q. 3 (page 534)
If three sides of a triangle are given, the Law of _________ is used to solve the triangle.
The solution is Cosines.
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Landscaping Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one
position on a flat path from the tree is 30掳, and from a second position 40 feet farther along this path it is 20掳. What is the height of the tree?
Constructing a Highway U.S. 41, a highway whose primary directions are north鈥搒outh, is being constructed along the west coast of Florida. Near Naples, a bay obstructs
the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The illustration shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay?
A surveillance satellite circles Earth at a height of h miles above the surface. Suppose that d is the distance, in miles, on the surface of Earth that can be observed from the satellite. See the illustration on the following page.
Part (a): Find an equation that relates the central angle u to the height h.
Part (b): Find an equation that relates the observable distance d and u.
Part (c): Find an equation that relates d and h.
Part (d): If d is to be miles, how high must the satellite orbit above Earth?
Part (e): If the satellite orbits at a height of miles, what distance d on the surface can be observed?
The angle of elevation of the Sun is 35.1掳 at the instant the shadow cast by the Washington Monument is 789 feet long. Use this information to calculate the height of the monument.
Finding Distances A forest ranger is walking on a path inclined at 5掳 to the horizontal directly toward a 100-foottall fire observation tower. The angle of elevation from the
path to the top of the tower is 40掳. How far is the ranger from the tower at this time?
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