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A vertical pole is divided into two segments such that the lower segment is one-third of the total height. From a point on the ground level, 20 m from the foot of the pole, the upper segment is seen under an angle whose tangent is 1/2. The possible total heights of the pole are

1. 20 m and 20√3 m
2. 20 m and 60 m
3. 16 m and 48 m
4. None of these

Correct answer: 20 m and 60 m

Solution

The correct option is right because the lower segment of the pole is one-third of the total height, and using the tangent of the angle from the observation point, we can derive two possible total heights that satisfy the given conditions, which are 20 m and 60 m.

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