Chapter 9.1, Problem 54STP

To determine

To find: The value of $\mathrm{d}$ .

Answer to Problem 54STP

The value of $\mathrm{d}$ is $33$ .

Explanation of Solution

Given information: The angles are $\mathrm{m}\angle \mathrm{E}=108,\mathrm{m}\angle \mathrm{F}=26$ and the side is $\mathrm{f}=20$ . The figure is shown below.

  

Calculation:

Consider the sum of triangle.

  $\begin{array}{l}\angle \mathrm{D}+\angle \mathrm{E}+\angle \mathrm{F}=180\\ \angle \mathrm{D}+108+26=180\\ \angle \mathrm{D}=46\end{array}$

Consider sine law.

  $\begin{array}{c}\frac{\sin \mathrm{F}}{\mathrm{f}}=\frac{\sin \mathrm{D}}{\mathrm{d}}\\ \frac{\sin 26}{20}=\frac{\sin 46}{\mathrm{d}}\\ \mathrm{d}=\frac{20\sin 46}{\sin 26}\\ \mathrm{d}=33\end{array}$