Answer to Question #320130 in Trigonometry for erica

Question

from the window of her condo, chang min measures an angle of elevation of 25 degrees to the top of the nearby building, 80 meters away. if the angle of depression to the foot of same building is 10 degrees. how tall is the nearby building?

Answer 1

The height of the building is equal to 

h=x+y

Using the trigonometric tangent identity.

Calculation of x

$tan(25^{\circ})=\dfrac{X}{80\;m}\\ tan(25^{\circ})\;80\;m=X\\ X=tan(25^{\circ})\;80\;m\\ X=37\;m\\$

Calculation of y.

$tan(10^{\circ})=\dfrac{Y}{80\;m}\\ tan(10^{\circ})\;80\;m=Y\\ Y=tan(10^{\circ})\;80\;m\\ Y=14\;m\\$

Evaluating numerically

$h=x+y\\ h=37\;m+14\;m\\ h=51\;m$

The height of the building is

$h=51\;m$