Question

Kehlani is trying to find the height of a radio antenna on the roof of a local building. she stands at a horizontal distance of 24 meters from the building. the angle of elevation from her eyes to the roof left bracket(point aaright bracket) is 20degrees ∘ , and the angle of elevation from her eyes to the top of the antenna left bracket(point bbright bracket) is 41degrees ∘ . if her eyes are 1.51 meters from the ground, find the height of the antenna left bracket(the distance from point aa to point bbright bracket). round your answer to the nearest tenth of a meter if necessary.

Answer 1

The height of the antenna is found to be 35.9 meters as she stands at a horizontal distance of 24 meters from the building.

we Label the point where Kehlani is standing as point A, the point where the antenna meets the roof as point B, and the point where Kehlani's line of sight meets the roof as point C.

Kehlani's distance from the building (AC) = 24 meters

Angle of elevation from Kehlani's eyes to the roof (∠ACB) = 20 degrees

Angle of elevation from Kehlani's eyes to the top of the antenna (∠ABC) = 41 degrees

Use the tangent function to find the height of the roof (BC):

tan(∠ACB) = BC/AC

tan(20°) = BC/24 meters

BC = 24 meters * tan(20°)

BC = 8.79 meters

F\We then find the height of the antenna (AB) using the tangent function :

tan(∠ABC) = AB/(BC + Kehlani's eye height)

tan(41°) = AB/(8.79 meters + 1.51 meters)

AB = (8.79 meters + 1.51 meters) * tan(41°)

AB = 35.89 meters