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An antenna stands on top of a 160 Ft building. From a point on the ground 118 Ft from the base of the building the angle of elevation to the top of the antenna is 58 degrees. Find the height of the antenna

Respuesta :

sqdancefan

Answer:

28.8 ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

The height to the top of the antenna is opposite the angle of elevation, and the distance to the building is adjacent. So, we have ...

tan(58°) = (160 ft +antenna height)/(118 ft)

(118 ft)·tan(58°) = 160 ft + antenna height . . . . . . . multiply by 118 ft

188.8 ft - 160 ft = antenna height = 28.8 ft . . . . . . subtract 160 ft, evaluate

The height of the antenna is 28.8 ft above the top of the building. (The total height of building + antenna is 188.8 ft.)

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