Question

I need help with this practice I am having trouble completing it

Answer 1

Using tangent function:

$\begin{gathered} \tan (24)=\frac{y}{x} \\ and \\ \tan (10)=\frac{y}{800+x} \end{gathered}$

so:

$\begin{gathered} y=\tan (24)\cdot x \\ \tan (10)=\frac{\tan(24)\cdot x}{800+x} \\ 800\tan (10)+x\tan (10)-x\tan (24)=0 \\ x(\tan (24)-\tan (10))=800\tan (10) \\ x=\frac{800\tan(10)}{\tan(24)-\tan(10)} \\ \end{gathered}$

Therefore,

$\begin{gathered} y=\tan (24)\cdot\frac{800\tan(10)}{\tan(24)-\tan(10)} \\ y\approx233.6ft \end{gathered}$

Answer:

Approximately 233.6 ft