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

The height of the building is 59 feet to the nearest whole number of feet.

We can use the tangent function to solve this problem. The tangent of an angle is equal to the opposite side over the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the distance from the car to the base of the building.

Let x be the height of the building

tan(32 degrees) = x / 90

x = 90 * tan(32 degrees)

x ≈ 59 feet

Therefore, the height of the building is 59 feet to the nearest whole number of feet.

Answer 2

Answer: The height of the building = 56 feet.

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 =(Perpenicular)/(base)\\\\\Rightarrow\ \tan 32^(\circ) =(AB)/(90)\\\\\Rightarrow\ 0.6248693519=(AB)/(90)\\\\\Rightarrow\ AB = 90* 0.6248693519=56.238241671\approx56`

Hence, the height of the building = 56 feet.