Question

Jada is visiting New York City to see the Empire State building. She is 100 feet away when she spots it. To see the top, she has to look up at an angle of 86.1 degrees. How tall is the Empire State building to the nearest foot?

Answer 1

1467 feets

Explanation:

Given that:

Horizontal Distance between jada and building = 100 feets

θ = 86.1°

Height, h of Empire state building =?

Using trigonometry :

Sinθ = opposite / Adjacent

Opposite = h

Adjacent = 100 feets

The angle of the top of the building to jada :

Sum of angles in a triangle ;

(90 + 86.1 + x) = 180

x = 180° - 176.1°

x = 3.90°

h = ( sin 86.1° * 100) / sin 3.90°

h = (0.9976842 * 100) / 0.0680152

h = 99.768427 / 0.0680152

h = 1466.8548

h = 1467 feets (nearest foot)

Hence, height of Empire state building is 1467 feets