Question

Analyze the diagram below and complete the instructions that follow.

Find m

Answer 1

D. 70.53

Explanation:

To solve this problem, one must use the right angle trigonometric rations. These ratios can be used to describe the ratio between the sides and an angle in a right triangle. Please note, each side is named relative to the angle that one is looking at, thus the same side can acquire different names based on the angle one uses to describe it. The trigonometric ratios are the following:

`sin(\theta)=(opposite)/(hypotenuse)\\\\cos(\theta)=(adjacent)/(hypotenuse)\\\\tan(\theta)=(opposite)/(adjacent)`

In this case, one is asked to find the measure of (<CBA), one is given the hypotenuse (the side opposite the right angle), and the side adjacent to this angle. Therefore, one should use the cosine (cos) function to find this angle.

`cos(\theta)=(adjacent)/(hypotenuse)`

Substitute,

`cos(CBA) = (3)/(9)`

Simplify

`cos(CBA) = (1)/(3)`

Inverse operations,

`CBA=cos^-1((1)/(3))`

Compute,

m<CBA = 70.53