Question

A man standing at the roof of a house finds the angle of depression to an object on the ground level as 45° If the distance between the base of the house to the object is 18√2 m, find the height of the house.​

Answer 1

Explanation:

Let the height of the house be "h".

Using the triangle formed by the object, the man, and the base of the house, and using the tangent function, we have:

tan(45°) = h / 18√2

h = (18√2) * tan(45°)

Since tan(45°) = 1,

h = 18√2 * 1 = 18√2 m

So the height of the house is 18√2 meters.

18√2 can be simplified to:

18 * √2 = 18 * 1.414 = 25.656 (approximately)