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

Solution:

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

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

Step 2: Evaluate the measure of angle B.

Thus, we have

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

Hence, to the nearest whole number, we have

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