Chapter 6.1, Problem 42E

To determine

Tofind:The distance from Gazebo to the dock.

Explanation of Solution

Consider the figure shown below.

  

The value of angle GTD is calculated as,

  $\begin{array}{c}74°=28°+\angle GTD\\ \angle GTD=46°\end{array}$

The value of $\angle GTA$ is calculated as,

  $\begin{array}{c}\angle GTA=90°-74°\\ =16°\end{array}$

Now, the value of $\angle TGA$ is calculated as,

  $\begin{array}{c}\angle TGA=180°-90°-16°\\ =74°\end{array}$

The measure of $\angle TGD$ is calculated as,

  $\angle TGD=65°$

And,

  $\begin{array}{c}\angle GDB=180°-90°-41°\\ =49°\end{array}$

The value of $\angle TDC$ is calculated as,

  $\begin{array}{c}\angle TDC=180°-90°-28°\\ =62°\end{array}$

And,

  $\begin{array}{c}\angle TDG=180°-62°-49°\\ =69°\end{array}$

Now apply the law of cosine.

  $\begin{array}{c}\frac{\sin 46°}{d}=\frac{\sin 69°}{100}\\ d=77.05\text{m}\end{array}$

Therefore, the distance from Gazebo to the dock is $77.05\text{m}$ .