Question

From a distance of 110 m, the angle of elevation to the top spire of a tower is 35°.

How high is the tower to the nearest metre

Answer 1

77 m

Explanation:

The geometry can be modeled by a right triangle. The distance from the viewpoint to the base of the tower is 110 m, the leg of the triangle adjacent to the angle. The height of the spire is the leg of the triangle opposite the given angle. The relevant trig relation is ...

Tan = Opposite/Adjacent

__

Using the given numbers, we find ...

tan(35°) = height/(110 m)

height = (110 m)tan(35°) = (110 m)×0.700208 ≈ 77.0 m

The height of the tower is about 77 meters.