Answers:
- Angle C = 68
- Side CB = 5.1
- Side CA = 13.7
The values of the side lengths are approximate.
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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.
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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.
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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
