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प्रश्न
The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y.
उत्तर
Let AB and CD be the two towers and E be the mid-point of AC.
Height of the tower, AB = y
Height of the tower, CD = x
it is given that, ∠ AEB=60° and ∠ CED=30°
Also, `AE=EC`
In right Δ AEB,
`tan 60°= (AB)/(AE)`
⇒ `sqrt3=y/(AE)`
`⇒ AE=y/sqrt3`
In right ∆CED,
`tan 60° = (AB)/(AF)`
⇒ `1/sqrt3=x/(CE)`
`⇒CE=sqrt3x`
`y/sqrtx=sqrt3x`
`⇒ y=3x`
`⇒x/y=1/3`
`∴ x: y=1:3`
Hence, the ratio of x : y is 1 : 3.
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