an observer 1.5meters tall is 20.5 metres away from a tower 22 metres high. determine the angle of elevation of the top of the tower from the eye of the observer

Tan A = Y/X = (22-1.5)/20.5 = 20.5/20.5 = 1.

A = 45o.

To determine the angle of elevation of the top of the tower from the eye of the observer, we can use trigonometry.

First, we can create a right triangle with the observer's eye as one vertex, the top of the tower as another vertex, and the base of the triangle as the distance between the observer and the tower.

Let's denote the height of the tower as 'h,' the distance between the observer and the tower as 'd,' and the angle of elevation as 'θ.'

Now, we can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle.

In this case, the opposite side is the height of the tower (h), and the adjacent side is the distance between the observer and the tower (d). Therefore, we have:

tan(θ) = h / d

Substituting the given values: h = 22 meters and d = 20.5 meters, we can now calculate the angle of elevation.

tan(θ) = 22 / 20.5

To solve for θ, we need to take the inverse tangent (or arctan) of both sides:

θ = arctan(22 / 20.5)

Using a calculator, we find θ to be approximately 47.31 degrees.

Therefore, the angle of elevation of the top of the tower from the observer's eye is approximately 47.31 degrees.