From the top of a hill 240 metres high, the angles of depression of the top and bottom of a pole are 30° and 60°, respectively. The difference (in metres) between the height of the pole and its distance from the hill is:
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Correct answer: D
Explanation
Given:
Height of the hill = 240 meters
Angle of depression of the base = 60°
Angle of depression of the top = 30°
Formula:
tanθ = Height / Distance
Let the distance of the pole from the hill = x
tan60° = 240 / x
√3 = 240 / x
x = 240/√3
= 80√3
Now the height of the pole = h
tan30° = (240 − h) / x
1/√3 = (240 − h) / (80√3)
240 − h = 80
h = 160
Difference = Distance − Height
= 80√3 − 160
= 80(√3 − 2)
= 80(2 − √3)