1. What is the measure of angle C? 2. What is the length of side CB? 3. What is the length of side CA?

Answers:

The values of the side lengths are approximate.

Work Shown:

Problem 1

A+B+C = 180

22+90+C = 180

112+C = 180

C = 180-112

C = 68

Or a slightly shorter method could involve these steps

A+C = 90

22+C = 90

C = 90-22

C = 68

This trick only works for right triangles.

Problem 2

With angle A as the reference angle, we know that

tan(angle) = opposite/adjacent

tan(A) = CB/AB

tan(22) = CB/12.7

12.7*tan(22) = CB

CB = 12.7*tan(22)

CB = 5.1311330681065

CB = 5.1

This value is approximate. I'm rounding to one decimal place since 12.7 is given to one decimal place.

Make sure your calculator is in degree mode.

Problem 3

We'll use the cosine ratio this time

cos(angle) = adjacent/hypotenuse

cos(A) = AB/CA

cos(22) = 12.7/CA

CA*cos(22) = 12.7

CA = 12.7/cos(22)

CA = 13.6973912320053

CA = 13.7

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