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Problem

A geographical surveyor places a marker at a position such that the angle between the horizontal and the top of a mountain is 45^o, after driving 1 km away from the mountain, the angle between the horizontal and the top of the mountain is 30^o.

Use the given information to find the height of the mountain.

Solution

Consider the diagram:

In the 45^o triangle, it is evident that x = h.

In the 30^o triangle, tan30^o = 1/3 = h/(x + 1), leading to x + 1 = 3h.

Therefore, h + 1 = 3h, 1 = 3h h, so h(3 1) = 1.

Hence, h = 1/(3 1) 1.36 km.