Multiple choice

The horizontal distance between two stations P and Q is 100 m. The vertical angles from P and Q to the top of a vertical tower at T are 30 and 50 above horizontal, respectively. The vertical angles from P and Q to the base of the tower are 0.10 and 0.50 below horizontal, respectively. Station P, Q and the tower are in the same vertical plane with P and Q being on the same side of T. Neglecting earth's curvature and atmospheric refraction, the height (in m) of the tower is

  1. 6.972

  2. 12.387

  3. 12.540

  4. 128.745
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A Correct answer
Explanation

Let h be the height of the tower. Using trigonometry, the height of the tower top above the horizontal plane of P and Q is H_top = d1 * tan(3) = d2 * tan(5). The base is H_base = d1 * tan(0.1) = d2 * tan(0.5). With d2 = d1 + 100, solving these simultaneous equations for the height difference gives the tower height.

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