Question

Use Right Triangle Trigonometry to solve for the measure of angles A and B. Round your answer to the nearest WHOLE NUMBER.

Answer 1

Given the triangle ACB below:

To solve for the measure of angles A and B, we use trigonometric ratios.

Provided that

`\begin{gathered} AB\Rightarrow hypotenuse \\ AC\Rightarrow opposite \\ CB\Rightarrow adjacent \end{gathered}`

Step 1: Evaluate the measure of angle A.

Thus, we have

`\begin{gathered} \cos\theta=(adjacent)/(hypotenuse) \\ \Rightarrow\cos A=(12)/(13) \\ cosA=0.92307 \\ take\text{ the cosine inverse of both sides,} \\ \cos^(-1)(\cos A)=\cos^(-1)(0.92307) \\ A=22.62\degree \\ \Rightarrow A\approx23\degree(nearest\text{ whole number\rparen} \end{gathered}`

Step 2: Evaluate the measure of angle B.

Thus, we have

`\begin{gathered} \sin B=(opposite)/(hypotenuse) \\ \Rightarrow\sin B=(12)/(13) \\ \sin B=0.92307 \\ take\text{ the sine inverse of both sides,} \\ \sin^(-1)(\sin B)=\sin^(-1)(0.92307) \\ B=67.38\degree \\ \Rightarrow B\approx67\degree \end{gathered}`

Hence, to the nearest whole number, we have

`\begin{gathered} \angle A=23\degree \\ \angle B=67\degree \end{gathered}`