A person is standing at a distance of 80m from a church looking at its top. The angle of elevation is of 45°.

Solution

Let’s denote the height of the church as “h”.

We can draw a right-angled triangle, where the person is standing at the base of the triangle, the top of the church is at the opposite side of the triangle, and the hypotenuse of the triangle is the line of sight from the person to the top of the church.

We can use the angle of elevation and the distance from the person to the church to find the height of the church.

From the triangle, we can see that:

tan(45°) = h/80

tan(45°) is equal to 1, so we can simplify the equation to:

1 = h/80

Multiplying both sides by 80, we get:

h = 80 meters

Therefore, the height of the church is 80 meters.