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The Application of Trigonometry

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1. Find the length L from point A to the top of the pole.
2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B?
3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far with the car travel in one minute?
4. A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.
5. What is the angle of elevation of the sun when a 35-ft mast casts a 20-ft shadow?
6. A V-gauge is used to find the diameters of pipes. In the figure on p. 373 in the text, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to predict the diameter.
a. Suppose that the diameter of a pipe is 2 cm. What is the distance VP?
b. Suppose that the distance VP is 3.93 cm. What is the diameter of the pipe?
c. Find the formula for d in terms of VP.
d. Find a formula for VP in terms of d.
The line VP is calibrated by listing the corresponding diameters as its units. This, in effect, establishes a function between VP and d.