Question

The angle of depression from a window 10m above the ground to a coin on the ground is 15°. a. Find the distance of the coin from the base of the building.
b. How far is the coin from the window.​

Answer 1

The distance of the coin from the base of building is 37.3 m.

What is angle of depression?

An angle of depression is stated to be formed by a horizontal line and the line that connects an item and the observer's eye. It is mostly used to determine the distance between the two objects when we are aware of the angles and height of an object above the ground.

Following is a list of the fundamental trigonometric ratio formulae, and both have the same formula for the angle of depression:

sin x = hypotenuse/perpendicular

base/hypotenuse = cos x

tan x = base/perpendicular

Let x serve as a representation of the distance from the coin to the building's base. When we use the necessary trigonometric function, we get:

Tan θ = perpendicular/base

Tan 15 = 10/x

0.2680 = 10/x

x = 10/0.2680

x  = 37.3134

x = 37.3 m

The distance of the coin from the base of the building is 37.3 m.

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