Question

From the top of an apartment building, the angle of depression to a car parked on the street below is 32 degree. The car is parked 90 feet from the base of the building. Find the height of the building to the nearest whole number of feet.

Answer 1

Answer: The height of the building = 56 feet.

Step-by-step explanation:

Let AB be the height of the building and BC be the distance of the car from the building on the ground.

Now , ∠ C = 32°   [Alternate interior angles ]

According to the trigonometry,

$\tan x =\dfrac{Perpenicular}{base}\\\\\Rightarrow\ \tan 32^{\circ} =\dfrac{AB}{90}\\\\\Rightarrow\ 0.6248693519=\dfrac{AB}{90}\\\\\Rightarrow\ AB = 90\times 0.6248693519=56.238241671\approx56$

Hence, the height of the building = 56 feet.