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

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a