# The Application of Trigonometry

Please view the attached file to see the diagram which accompanies this question.

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.

#### Solution Summary

This solution is comprised of detailed explanations of the application of the trigonometric functions such as sine, cosine, and tangent. With diagrams and step-by-step contents, the solution should provide the students a clear understanding of trigonometric functions in real life.