Question

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

Answer 1

Answer:

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

Step-by-step 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;

$Tan(\theta) = \dfrac{Opposite \, side \, to\ angle}{Adjacent\, side \, to\, angle}$

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

$Tan(15 ^{\circ}) = \dfrac{The \ distance \, of \, the \ overpass \ above \ ground}{100 \ ft}$

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