Multiple choice

The upper part of a tree, broken over by the wind, makes an angle of 60° with the ground. The distance between the root and the point where the top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?

  1. 84.14

  2. 93.3

  3. 98.25

  4. 120.24
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B Correct answer
Explanation

Let the broken part be h and the standing part be x. The distance from the root is 25. tan(60) = h/25 is incorrect; rather cos(60) = 25/hypotenuse, so hypotenuse = 50. tan(60) = height_standing / 25, so height_standing = 25 * sqrt(3) = 43.3. Total height = 50 + 43.3 = 93.3.

AI explanation

The broken tree forms a right-angled triangle where the base is 25 meters and the angle at the ground is 60 degrees. Using trigonometric ratios, the intact stem height is 25 multiplied by tan 60, which equals 25 times the square root of 3. The length of the broken upper part is 25 divided by cos 60, which is 50 meters. The total height is the sum of 25 times the square root of 3 and 50, which approximates to 93.3 meters.

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