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A radio tower is located 325 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 24" and that the angle of depression to the bottom of the tower is 22° . How tall is the tower? Give your answer rounded to the nearest foot.



Answer :

sqdancefan

Answer:

  276 ft

Step-by-step explanation:

You want to know the height of a radio tower located 325 ft from a building if the angles of elevation and depression to the top and bottom of the tower from a window in the building are 24° and 22°, respectively.

Tangent

The tangent relation is ...

  Tan = Opposite/Adjacent

In the attached diagram, we can use this relation twice: once to find the height of the top of the tower above the window, and once to find the distance to the bottom of the tower below the window.

  tan(24°) = TX/WX
  tan(22°) = BX/WX

Solving for the unknown lengths, we have ...

  TX = WX·tan(24°)
  BX = WX·tan(22°)

So the tower height is ...

  BT = BX +TX

  BT = 325·(tan(22°) +tan(24°)) ≈ 276.0 . . . . . feet

The tower is about 276 feet tall.

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