Analyze the diagram below and complete the instructions that follow. find m

70.5°

Solution:

Call B, the measure of the angle CBA

cos(B) = adjacent-leg / hypotenuse = 3 / 9 = 1 / 3

=> B = arc cos (1/3) ≈ 70.5°

I will calculate other measures for you, trying to cover the most common ratios: sine, cosine, tangent

1) (segment CA)^2 + (segment BC)^2 = (hypotenuse)^2

=> (segment CA )^2 = (hypotenuse)^2 - (segment BC)^2 = 9^2 - 3^2 = 81 - 9 = 72

=> segment CA = √72 = 6√2

2) sin(B) = opposite-leg / hypotenuse = 6√2 / 9 =2√2 / 3

3) sin(A) = cos(B) = 1/3

4) cos(A) = sin(B) = 2√2 / 3

5) tan(B) = opposite-leg / adjacent-leg = (2√2 / 3 ) / 3 = 2√2 / 9

6) tang(A) = 3 / (2√2 /3) = 9 /( 2√2) = 9√2 / 4

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