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JEE Main20206 Sep 2020Morning ShiftMathematicsHeights and DistancesActual

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45 ° . After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30 ° to the horizontal plane the angle of elevation of the top of the hill becomes 75 ° . Then the height of the hill (in meters) is _____.

Correct answer

0

Step-by-step solution

x = 80 cos 30 ° = 40 3 y = 80 sin 30 ° = 40 tan 45 ° = 1 ⇒    x + z = h ⇒    40 3 + z = h tan 75 ° = h - y z ⇒    2 + 3 = h - 40 z ⇒    z = h - 40 2 + 3 ⇒    h - 40 3 = h - 40 2 + 3 ( 1 + 3 ) h = 80 ( 1 + 3 ) h = 80

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