The angle of elevation of a building 80 m high from a man on the ground is 50.41 degrees. How far is the man from the building?

Question

The angle of elevation of a building 80 m high from a man on the ground is 50.41 degrees. How far is the man from the building?

Answer 1

Solution:

This is a very simple trigonometry question. The ground, the building, and the angle of elevation represent a right angle triangle with an angle α of 50.41° between the hypotenuse(The line of sight from the man's eye to the top of the building) and the ground. The tangent of this angle is the opposite which is the building elevation of 80m divided by the adjacent which is the unknown horizontal distance between the man and the building. This distance denoted by X is what we are looking to determine.

In math form, we have the equation tanα = 80 m / X and X (tanα) = 80m divide by tanα

X = 80m / tanα = 80m / tan 50.41° = 66.2 m