Question

An engineer, in an attempt to make a quick measurement, walks 100 ft from the base of an overpass

and determines that the angle of elevation to the overpass is 15°. Draw a diagram and solve for the
distance the overpass is above the ground.

Answer 1

The distance of the overpass above the ground is approximately 26.795 ft

Explanation:

The parameters given are;

The distance from the overpass the engineer stands before determining the angle of elevation of the overpass from his standing point = 100 ft

The angle of elevation of the overpass as determined by the engineer from 100 ft = 15°

By trigonometric ratios, we have;

`Tan(\theta) = (Opposite \, side \, to\ angle)/(Adjacent\, side \, to\, angle)`

The opposite side to the 15° angle of elevation in the above case is the distance of the overpass above the ground

The opposite side to the 15° is the distance of the engineer from the base of the overpass

Therefore;

Tan(15°) the height of the overpass=

length

`Tan(15 ^(\circ)) = (The \ distance \, of \, the \ overpass \ above \ ground)/(100 \ ft)`

The distance of the overpass above the ground = 100 × tan (15°) ≈ 26.795 ft.