Answer to Question #209906 in Trigonometry for sop

Question

from the top of an 80 ft building the angle of elevation of the top of the taller building is 49 degrees and the angle of depression of the base of this building is 62 determine the height of the taller building to the nearest foot

Answer 1

$let\ d\ be\ the\ distance\ between\ the\ buildings$

$let\ l\ be\ the\ difference\ between\ the\ height\ of\ the\ buildings$

$\tan{\left(62^{\circ}\right)}=\frac{80}{d}=>d=\frac{80}{\tan{\left(62^{\circ}\right)}}$

$\tan{\left(49^{\circ}\right)}=\frac{l}{d}=\frac{l\tan{\left(62^{\circ}\right)}}{80}$

$l=\tan{\left(49^{\circ}\right)}\ast\frac{80}{\tan{\left(62^{\circ}\right)}}=48.9ft$

$height\ of\ the\ taller\ building\ \approx\ 49+80=129 ft$