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# Find the length L from point A to the top of the pole.

A.

As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representations used.

1. Find the length L from point A to the top of the pole.

b

L 28ft

60

A C

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.

Suppose that the diameter of a pipe is 2 cm. What is the distance VP?
Suppose that the distance VP is 3.93 cm. What is the diameter of the pipe?
Find the formula for d in terms of VP.
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.

Reference:
Bittinger, M. L., & Beecher, J. A. (2000). Trigonometry update. Reading, MA: Addison Wesley.

B.

You are interviewing for a position with an association representing the tire industry. The federal government mandates safety testing of all tires manufactured in the United States. Recently there has been concern that the rubber used in the tires could deteriorate while in store inventories. In September 2003, a safety group asked the U.S. government to require expiration dates for tires. Representatives for the manufacturing industry test the tires, collect data, and create graphs of functions to test tire durability. As part of the interviewing process, you are asked to solve the following problems.

Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why?
Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas but can be simplified by using the sine and cosine formulas.
What is the difference between a trig equation that is an identity and a trig equation that is not an identity? Provide an example to clarify.

#### Solution Summary

This solution is comprised of a detailed explanation to find the length L from point A to the top of the pole.

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