From the top of a pole, the angles of depression of two objects P and Q situated on the same side are 30 degree and 45 degree separated by a distance of 100 m. What will be the height of this pole?

From the top of a pole, the angles of depression of two objects P and Q situated on the same side are 30 degree and 45 degree separated by a distance of 100 m. What will be the height of this pole? Correct Answer 100 / (√3 – 1) m

Let the height of the pole = h m, base distance of the point having 45 degree = x m. ➩ tan 45 = height / base distance ➩ 1 = h / x ➩ h = x Also, ➩ tan 30 = height / base distance ➩ 1 / √3 = h / (x + 100) ➩ x + 100 = h√3 On substituting x from the above equation, ➩ h + 100 = h√3 ➩ 100 = h (√3 – 1) ➩ h = 100 / (√3 – 1) m
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