A flag pole 25 ft tall stands on top of the building. From a point in the same horizontal plane with the base of the building, the angles of elevation of the top and bottom of the flag pole are 62 degrees and 56 degrees respectively. How high is the building?

Originally Posted by fayeorwhatsoever

A flag pole 25 ft tall stands on top of the building. From a point in the same horizontal plane with the base of the building, the angles of elevation of the top and bottom of the flag pole are 62 degrees and 56 degrees respectively. How high is the building?

1. Draw a sketch.

2. You are dealing with 2 right triangles. Use Tangens to determine the distances:

$\displaystyle \dfrac hx = \tan(56^\circ)$ will yield $\displaystyle x=\dfrac h{\tan(56^\circ)}$

Plug in this term into the second equation:

$\displaystyle \dfrac{h+25}x=\tan(62^\circ)$ will yield: $\displaystyle \dfrac{h+25}{\dfrac h{\tan(56^\circ)}}=\tan(62^\circ)~\implies~ h\tan(56^\circ)+25 \tan(56^\circ)=h\tan(62^\circ)$

Finally you get: $\displaystyle h=\dfrac{25\tan(56^\circ)}{\tan(62^\circ)-\tan(56^\circ)} \approx 93.1$