# Trigonometry : Angles and Lengths

MTH212

Unit 5 Individual Project - A

1. The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive full credit.

Work shown here:

2. An A-frame lake house is 15 feet wide. If the roof of the home makes a angle with the base of the home, what is the length of the house from ground level to the peak of the roof? Round final answer to the nearest foot.

3. Use common trigonometric identities for the functions given to find the indicated trigonometric functions. (Hint: Remember the reciprocal properties of sine, cosine, and tangent.) Show all work to receive full credit.

A. If and , what are the values of

a) =

b) =

c) =

B. If and , what are the values of

a) =

b) =

c) =

4. Solve the following application problem. Show all work to receive full credit.

A. A man at ground level measures the angle of elevation to the top of a building to be . If, at this point, he is 15 feet from the building, what is the height of the building?

Draw a picture, show all work, and find the solution. Round to the nearest hundredths.

B. The same man now stands atop a building. He measures the angle of elevation to the building across the street to be and the angle of depression (to the base of the building) to be . If the two buildings are 50 feet apart, how tall is the taller building? See the following figure. Round to the nearest hundredths.

6. A weather balloon B lies directly over a 1500-meter airstrip extending from A to C.

The angle of elevation from A to B is and from C to B is (Larson, Hostetler, Edwards, 2005).

Find the distances from A to B and from C to B. Show all work to receive full credit. Round to the nearest hundredths.

Reference

Larson, R., Hostetler, R. P., & Edwards, B. H. (2005). Trigonometry a graphing approach (4th ed.). Boston: Houghton Mifflin.

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#### Solution Summary

Angles and lengths are found through trigonometry.