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?
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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
