SOLUTION: The angle of elevation of the top of the tower at a distance 40m from it is the compliment of the angle of elevation of the same tower a distance of 120m from it. Compute the heigh

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Question 1170274: The angle of elevation of the top of the tower at a distance 40m from it is the compliment of the angle of elevation of the same tower a distance of 120m from it. Compute the height of the tower. Use sine or cosine law
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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tan(a) = h%2F40


tan(b) = h%2F120


a + b = pi%2F2  ====>  a = pi%2F2 - b


tan(a) = tan%28pi%2F2-b%29 = 1%2Ftan%28b%29  ====>


h%2F40 = 1%2F%28%28h%2F120%29%29 = 120%2Fh  ====>


h%5E2 = 40*120 = 40*40*3


h = sqrt%2840%2A40%2A3%29 = 40%2Asqrt%283%29 = 69.282 meters.    ANSWER

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