Answer to Question #106108 in Trigonometry for trin

Question

From the window in a nearby building, the angle of elevation to the top of an apartment building is 28°. The angle of depression from the same window to the bottom of the apartment building is 34°. The window is 24 feet above the ground. How tall is the apartment building?

Answer 1

As per the given question,

angle of elevation =$28^\circ$

angle of depression from the same window to the bottom of the building $=34^\circ$

The height of the window from the bottom(h) =24 feet

Let height of the building from the level of window is h'

For the depression from the window,

Let the distance between the building is x,

So, $\tan 34^\circ=\dfrac{h}{x}$

$x=\dfrac{24}{\tan 34^\circ}=35.58 feet$

Now, similarly,

For the above from the window,

$\tan 28^\circ=\dfrac{h'}{x}$

$\Rightarrow h'=x\tan 28^\circ feet$

$\Rightarrow h'=35.58\times tan(28^\circ)=18.92 feet$

Hence total height of the building = h+h'

$=24+18.92=42.92 feet$