Multiple choice

A parachutist is descending vertically and makes angles of elevation of 45$^{\circ}$ and 60$^{\circ}$ at two observation points 100 m apart from each other on the side to his left. The approximate height from which he falls and the approximate distance of the point where he falls on the ground from the first observation point are respectively.

  1. 136.61, 1336.01

  2. 236.0, 136.61

  3. 236.60, 336.01

  4. 236.60, 236.61
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D Correct answer
Explanation

Let h be height and d be distance from first point. tan(45) = h/d = 1 => h=d. tan(60) = h/(d-100) = sqrt(3). So h = sqrt(3)*(h-100) => h = h*sqrt(3) - 100*sqrt(3) => h(sqrt(3)-1) = 100*sqrt(3). h = 100*sqrt(3) / (sqrt(3)-1) = 100*1.732 / 0.732 = 173.2 / 0.732 = 236.6. d = 236.6. The distance from the first point is 236.6.

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