Answer:
592.4 feet
Step-by-step explanation:
The cross section of the tower can be modeled by a hyperbola with its vertex at (x, y) = (100, 360) and its center at (0, 360). The point (x, y) = (200, 0) helps define the equation of it.
Basic form:
((x -h)/a)^2 -((y -k)/b)^2 = 1
Filling in (h, k) = (0, 360) and a=100, we can find b using the given point:
(200/100)^2 -((0-360)/b)^2 = 1
(360/b)^2 = 3 . . . . . . . . . . . . . . . rearrange, simplify
b^ = 360^2/3 = 43200
So, the equation of the hyperbola is ...
x^2/10000 - (y-360)^2/43200 = 1
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Then for x = 150 (the distance from center at the top, we can find y to be ...
(150/100)^2 - (y -360)^2/43200 = 1
1.25 = (y -360)^2/43200
y = 360 +√(1.25·43200) ≈ 592.379
The height of the tower is about 592.4 feet.
