A 50 ft flagpole is mounted to the top of a building. If the angle of elevation from a spot on the street to the top of the pole is 58 degrees and the angle of elevation from the same spot to the bottom of the pole is 46 degrees, find the height of the building.

the height of the building = 91.67161722 feet.

Step-by-step explanation:

Suppose the height of the building (BC) = X feet.

A 50 ft flagpole (AB) is mounted to the top of a building.

So, height of the top of flag above the ground (AC) = (X+50) feet.

If the angle of elevation from a spot (P) on the street to the top of the pole is 58 degrees and the angle of elevation from the same spot (P) to the bottom of the pole is 46 degrees.

It means ∠APC = 58° and ∠BPC = 46°.

Considering Right triangle ΔACP, cot (∠APC) = PC / AC.

PC = AC*cot (∠APC) = (X+50) * cot (58°)

Considering Right triangle ΔBCP, cot (∠BPC) = PC / BC.

PC = BC*cot (∠BPC) = X*cot (46°)

We have PC = PC.

X*cot (46°) = (X+50) * cot (58°)

0.965688774 * X = 0.624869351 * (X+50)

(0.965688774 - 0.624869351) * X = 0.624869351 * 50

0.340819422 * X = 31.2434676

X = 31.2434676 / 0.340819422 = 91.67161722 feet.

Hence, the height of the building = 91.67161722 feet.