A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100 m further in line with the tower, it subtends an angle of 30 o at the point. Then, the height of the tower is

Question

A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100 m further in line with the tower, it subtends an angle of 30 o at the point. Then, the height of the tower is, 20 3 m, 30 3 m, 50 3 m, 10 3 m

MARKS App · Accepted Answer

From ∆ A B D and ∆ A C D , tan 60 o = H x , tan 30 o = H x + 100 ⇒ H tan ⁡ 60 ° = H tan ⁡ 30 ° - 100 ⇒ H 3 = H 1 3 - 100 ⇒ 3 H - H 3 = 100 ⇒ 3 H - H = 100 3 ⇒ H = 50 3 m

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