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A pole of certain height is standing on the top of a tower. The height of the tower is 150 meters. If the pole makes an angle of tan-1(1/5) at a point O, which is 120 meters away from the foot of tower, then what will be the distance between point O and the top of pole?

A pole of certain height is standing on the top of a tower. The height of the tower is 150 meters. If the pole makes an angle of tan-1(1/5) at a point O, which is 120 meters away from the foot of tower, then what will be the distance between point O and the top of pole? Correct Answer 261 m

GIVEN:

The height of the tower is 150 meters.

Point O is 120 meters away from the foot of tower.

CONCEPT:

Application of trigonometric ratios.

FORMULA USED:

tanA = Perpendicular/Base

tan (x + y) = (tan x + tan y) / (1 – tan x tan y)

CALCULATION:

From the given information the diagram can be drawn as

/ = (150 + a)/120

⇒ 29/15 = (150 + a)/120

⇒ a = 82

Now the distance between point O and the top of pole (C):

⇒ (CO)2 = (150 + 82)2 + (120)2

⇒ (CO)2 = 68224

⇒ CO = 261 mt (approx.)

∴ distance between point O and the top of pole is 261 mt

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