Question

Building A is 480 feet and building B is 654 feet tall. if the angle of depression from building B to building A is 42 degree , how far apart are the buildings

Answer 1

First of all, we draw the buildings..

We need to find the value of x, yellow color in the draw... to do that, I need to apply

$\tan A=\frac{y}{x}$

The value of y, will be:

$\begin{gathered} y+480=654 \\ y=654-480 \\ y=174 \end{gathered}$

Finally, with the value of A=42 and y = 174

$\begin{gathered} \tan 42=\frac{174}{x} \\ x=\frac{174}{\tan 42}=\frac{174}{0.9}=193.33 \\ x=193.33 \end{gathered}$

And the building A is 193.33 feet until the building B.