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प्रश्न
On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.
उत्तर
Let AB be the tower of height 150 m and Two objects are located when the top of the tower are observed, makes an angle of depression from the top and bottom of the tower are 45° 60° respectively.
Let CD = x, BD = y, ∠ADB = 60°, ∠ACB = 45°
So we use trigonometric ratios.
In a triangle ABC,
`tan 45^@ = 150/(x + y)`
`=> x = y = 150` ......(1)
Again in a triangle ABD,
`tan 60^@ = 150/y`
`=> sqrt3 = 150/y`
`=> sqrt3 = 150` ......(2)
So from (1) and (2) we get
`x + 150/sqrt3 = 150`
`=> sqrt3x = 150(sqrt3 - 1)`
`=> x = 63.39`
Hence the required distance is approximately 63.4 m
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