From a point exactly midway between the feet of two vertical towers standing on level ground, the angles of elevation of their tops are 30° and 60°. The ratio of the height of the first tower to the height of the second is:

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Accepted Answer

1 : 3. Both towers are the same distance d away, so their heights are d·tan30° = d/√3 and d·tan60° = √3d. The ratio is (1/√3) : √3 = 1 : 3. Comparing the angles rather than their tangents suggests the wrong 1 : 2, and forgetting to divide gives 1 : √3.

From a point exactly midway between the feet of two vertical towers standing on level ground, the angles of elevation of their tops are 30° and 60°. The ratio of the height of the first tower to the height of the second is:

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