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;
[tex]Tan(\theta) = \dfrac{Opposite \, side \, to\ angle}{Adjacent\, side \, to\, angle}[/tex]
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
[tex]Tan(15 ^{\circ}) = \dfrac{The \ distance \, of \, the \ overpass \ above \ ground}{100 \ ft}[/tex]
The distance of the overpass above the ground = 100 × tan (15°) ≈ 26.795 ft.
