From a point on the roof of a building 22 mt. height it is observed that the angles of depression of the top and foot of a lamp post are 30 degree and 60 degree respectively . what is the height of the lamp post ?
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Answer:
Height of the lamp post ≈ 14.667 ft.
Step-by-step explanation:
Let, foot of the lamp post be d metres away from the foot of the building.
So, tan 60° = (√3) = (22 / d)
or, d = (22 / √3)
Now, tan 30° = (1 / √3) = (22 - l) / d
or, (22 - l) = d * (1 / √3) = (22 / 3)
l = 22 - (22 / 3) = (44 / 3)
l ≈ 14.667
Height of the lamp post ≈ 14.667 ft.
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