A tree is broken by the wind. The top struck the ground at an angle of 30c and at distance of 10 m from its root.The whole height of the tree is
Question
A tree is broken by the wind. The top struck the ground at an angle of 30° and at distance of 10 m from its root. The whole height of the tree is
Solution
The problem can be solved using trigonometry. The situation forms a right triangle where the tree is the hypotenuse. The angle given is 30 degrees and the adjacent side (distance from the root to where the top struck) is 10 m.
We know that the cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse.
So, cos(30) = 10/hypotenuse
We can rearrange this to solve for the hypotenuse (which is the height of the tree):
hypotenuse = 10 / cos(30)
Using a calculator, we find that cos(30) is approximately 0.866.
So, hypotenuse = 10 / 0.866 = approximately 11.55 meters.
Therefore, the whole height of the tree is approximately 11.55 meters.
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