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A man observes that when he moves up a d...

A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is `30^(@)`, and when he moves up further a distance c metres the angle of depression of that point is `45^(@)`. The angle of inclination of the slope with the horizontal is
(Man starts from bottom of slope)

A

`60^(@)`

B

`45^(@)`

C

`75^(@)`

D

`30^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Applying m - n theorem of trigonometry
we get

`(c + c) cot (theta-30^(@))c cot 15^(@) - c cot 30^(@)`
or `cot (theta -30^(@)) = 1`
`= theta - 30^(@) = 45^(@)`
`:. theta = 75^(@)`
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