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A tower and a pole are certain distance apart and angle of depression from the top of pole to the foot of tower is 30°. Angle of depression of foot of pole for top of tower is 60° and if height of pole is 30 feet, then what is the height of tower?

A tower and a pole are certain distance apart and angle of depression from the top of pole to the foot of tower is 30°. Angle of depression of foot of pole for top of tower is 60° and if height of pole is 30 feet, then what is the height of tower? Correct Answer 90 feet

GIVEN:

Angle of depression from the top of pole to the foot of tower = 30°

Angle of depression of foot of pole for top of tower = 60°

Height of pole = 30 feet

FORMULA USED:

tan θ = Perpendicular/Base

CALCULATION:

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∠PSQ = 60° and ∠RQS = 30°

RS = 30 feet

tan 30° = RS/QS

1/√3 = 30/QS

⇒ QS = 30√3

tan 60° = PQ/QS

√3 = PQ/30√3

⇒ PQ = 30√3 × √3

PQ = 90 feet

∴ Height of tower is 90 feet

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