Multiple choice

The upper part of a tree is broken over by the wind makes an angle of $\displaystyle 30^{\circ} $ with the ground and the distance from the root to the point where the top of the tree meets the ground is 15 m The height of the broken part is

  1. $\displaystyle 15\sin 30^{\circ}m $
  2. $\displaystyle 15\cos 30^{\circ}m $
  3. $\displaystyle 15\tan 30^{\circ}m $
  4. $\displaystyle 15\sec 30^{\circ}m $
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D Correct answer
Explanation

The tree forms a right triangle where the distance from the root to the tip is the adjacent side (15m) and the broken part is the hypotenuse. The angle is 30 degrees. cos(30) = adjacent/hypotenuse = 15/hypotenuse. So, hypotenuse = 15/cos(30) = 15 * sec(30).

AI explanation

For the broken upper part of the tree, it acts as the hypotenuse of a right-angled triangle where the adjacent side to the 30-degree angle is the ground distance of 15 meters. Using the cosine ratio, cos(30 degrees) equals 15 divided by the height of the broken part. Rearranging this equation gives the height as 15 divided by cos(30 degrees), which is equivalent to 15 sec(30 degrees) meters.

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