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A surveyor measures the angle of elevation to the top of a building to be 70 degrees. The surveyor then walks 50 ft farther from the base of the tower and measures the angle of elevation to be 50 degrees. The surveyor's angle-measuring device 5.5 ft from the ground. How tall is the building, to the nearest foot?

Feb 19, 2020

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A surveyor measures the angle of elevation to the top of a building to be 70 degrees. The surveyor then walks 50 ft farther from the base of the tower and measures the angle of elevation to be 50 degrees. The surveyor's angle-measuring device 5.5 ft from the ground. How tall is the building, to the nearest foot?

We'll add the  5.5 ft  to the end result  of  H

Let  D  be the original distance  from the  building    and  H be the remaining bldg height

So

tan ( 70°) =   H / D    ⇒  D =  H / tan (70)

And we know that

tan (50)  =     H / [ 50 + D ]

50 + D  = H / tan (50)          sub for D

50  + H /tan (70)  = H / tan (50)

50  =  H [ 1/tan (50)  - 1/tan (70)]

H =   50  / [ 1/tan (50)  -1/tan(70)  ]  ≈  105.2 ft

Adding 5.5  ft to this gives us     ≈ 110.7 ft =  111 ft  =  bldg height

Feb 19, 2020
edited by CPhill  Feb 19, 2020