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From the top of a hill 400 meters high the angle of depression of the top and the bottom of a pillar on the level ground are 30° and 60°, respectively. Then, what is the height of the pillar?

From the top of a hill 400 meters high the angle of depression of the top and the bottom of a pillar on the level ground are 30° and 60°, respectively. Then, what is the height of the pillar? Correct Answer <span lang="EN-IN" style=" line-height: 107%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">800 / 3 m</span>

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PQ is the height of the hill and AB is height of the pillar.

Suppose, CQ = h

In ΔBCQ -

⇒ tan 30° = h / BC

⇒ 1 / √3 = h / BC

⇒ BC = h√3       ----(1)

In ΔAPQ -

⇒ tan 60° = PQ / AP

⇒ √3 = 400 / AP

⇒ AP = 400 / √3

∴ AP = BC

Thus, h√3 = 400 / √3

⇒ h = 400 / 3

∴ The height of the pillar = 400 - 400 / 3 = 800 / 3 m

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