Chapter 8.7, Problem 5ST2

To determine

To find $m\angle D$ by using the triangle shown below.

  

Answer to Problem 5ST2

  $D={74}^{\circ }$

Explanation of Solution

Given:

  

Calculation:

In the given triangle,

  $\begin{array}{l}\tan D=\frac{\text{opposite}}{\text{adjacent}}\\ \Rightarrow \tan D=\frac{24}{7}\\ \Rightarrow D={\tan }^{-1}\left(\frac{24}{7}\right)\\ \Rightarrow D={73.7397}^{\circ }\\ \Rightarrow D\approx {74}^{\circ }\end{array}$