A person observes the top of a tower at an angle of elevation 30°. After walking 20 m towards the tower, the angle becomes 60°. Find the height of the tower.
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A person observes the top of a tower at an angle of elevation 30°. After walking 20 m towards the tower, the angle becomes 60°. Find the height of the tower.

G1 Physics · Accepted Answer

Let the nearer distance from the tower be x and height be h. From the nearer point, tan60°=h/x, so h=√3x. From the first point the distance is x+20 and tan30°=h/(x+20), so h=(x+20)/√3. Equating: √3x=(x+20)/√3 ⇒ 3x=x+20 ⇒ x=10. Hence h=10√3 m.