Question

An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a buliding. The angle of elevation to the top of the building is 22°. The engineer knows the building is 450 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot?

Answer 1

$\tan( \alpha ) \: = \: \frac{h}{b}$
$\alpha \: = \: {22}^{0}$
$h \: = \: 450 \: ft$
Therefore,
$b \: = \: h \cot( \alpha )$
$b \: = \: 450 \: ft \: \times \: \cot( {22}^{0} )$
b = 450 ft × 2.47508685
b = 1,113.78908 ft
or,
b ≈ 1,114 ft.