Chapter 8.7, Problem 48STP

To determine

To select:

The correct option to measure of $\angle A$ to

A. $32.2$

B. $51.1$

C. $38.9$

D. $57.8$

Answer to Problem 48STP

The correct option is C. The measure of $\angle A$ is $38.9°$

Explanation of Solution

Given information:

  

Calculation:

If is a $△ABC$ right triangle with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of the length of

leg opposite $\angle A$ to the length of the leg adjacent $\angle A$ .

  

As per the definition of tangent, $\angle A$ is calculated as:

  $\begin{array}{l}\sin A=\frac{32}{35}\\ \angle A={\sin }^{-1}\left(\frac{32}{35}\right)\\ \angle A=38.9°\end{array}$

The correct option is C.