Chapter 8.5, Problem 30WE

To determine

To find: the length of EF .

Answer to Problem 30WE

The length of EF is 230.

Explanation of Solution

Given:

The triangles with dimensions are shown below:

  

Calculation:

In triangle DGF ,

  $\begin{array}{c}\tan 32°=\frac{GF}{DF}\\ \frac{GF}{DF}=0.625\mathrm{......}\left(1\right)\end{array}$

In triangle EFG ,

  $\begin{array}{c}\tan 44°=\frac{GF}{EF}\\ \frac{GF}{EF}=0.9656\mathrm{......}\left(2\right)\end{array}$

Divide the equation (1) by (2) as follows:

  $\begin{array}{l}\frac{\frac{GF}{DF}}{\frac{GF}{EF}}=\frac{0.625}{0.9656}\\ \frac{EF}{355}=0.647\\ EF=0.647\times 355\\ EF\approx 230\end{array}$

Hence, the length of EF is 230.