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Question

A , B , C are three collinear points on the ground such that B lies between A and C and AB=10 m. If the angles of the elevation of the top of a vertical tower standing at C are respectively 300 and 600 as seen from A and B, then the height of the tower is

A
53m
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B
5m
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C
1033
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D
2033
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Solution

The correct option is B 5√3mLet A,B,C be the points on ground and PC be the vertical tower.Let BC=x m∴AC=(x+10) m In ΔPCB,∠PCB=90°,∠PBC=60°∴tan60°=PCBC√3=PCx∴PC=x√3m→(1)In ΔPCA,∠PCA=90°,∠PAC=30°tan30°=PCAC=PCAB+BC⇒1√3=PC10+x⇒PC=(10+x)√3m→(2)From (1)&(2)x√3=10+x√33x=10+x2x=10⇒x=5m∴ Height of tower (PC)=5√3m

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