Arturo O. answered • 07/12/16

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Based on how I interpret the given information, the observer at B is at a distance 150 + x from the tower, and sees the top at the lower angle of 32 degrees from the horizontal, while the observer at A is at a distance x from the tower, and sees the top at the steeper angle of 40 degrees from the horizontal. Then we can get the height h from

h/x = tan(40) = 0.8391

h / (150 + x) = tan(32) = 0.6249

We have 2 unknowns x and h, and 2 equations. Get x = h/0.8391 from the top equation and substitute into the bottom equation to obtain h.

h / (150 + h/0.8391) = 0.6249

h / (150 + 1.1918h) = 0.6249

h = 0.6249 (150 + 1.1918h)

h = 93.735 + 0.7448h

h = 93.735 / (1 - 0.7448) = 367.3 ft

We can also get x

h/x = 0.8391 ⇒ x = h/0.8391 = 367.3/0.8391 = 437.7 ft