From a point on the ground, the angle of elevation of the top of a tower is 60°. From another point 20 m farther away on the same straight line, the angle is 30°. Find the distance of the nearer point from the tower.
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Question

From a point on the ground, the angle of elevation of the top of a tower is 60°. From another point 20 m farther away on the same straight line, the angle is 30°. Find the distance of the nearer point from the tower.

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G1 Physics · Accepted Answer

Let the nearer distance be x and tower height h. h=x tan60°=√3x. From the farther point, h=(x+20)tan30°=(x+20)/√3. Equating gives 3x=x+20, so x=10 m.