The angle of depression from the top of a storey building to a stationary car is 50m from the base of the is 30 degrees . Calculate the height of the building ?

Let's denote the height of the building as h.

From the information given, we can form a right triangle with the height of the building as the opposite side, the distance from the base of the building to the car as the adjacent side, and the angle of depression as 30 degrees.

Using trigonometry, we can use the tangent function to find the height of the building:

tan(30 degrees) = h / 50m

tan(30 degrees) = h / 50

h = 50 * tan(30 degrees)

h = 50 * 0.5774

h = 28.87 meters

Therefore, the height of the building is approximately 28.87 meters.

Here is the solution for calculating the height of the building:

Given:
Angle of depression, θ = 30 degrees
Distance from the building to the car, d = 50 m

We can use the tangent function to find the height of the building (h):

tan θ = h/d
Substituting the given values:
tan 30° = h/50
h = 50 tan 30°
h = 50 - 0.5774 (using a calculator)
h = 28.87 m

Therefore, the height of the building is approximately 28.87 meters.