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 ( . )3 1 732=(a) m10 3 (b) m3 10(c) m20 3 (d) m
Question
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 ( . )3 1 732=(a) m10 3 (b) m3 10(c) m20 3 (d) m
Solution
The problem describes a right triangle, where the broken tree forms the hypotenuse. The angle given is 30 degrees, the distance from the root to where the top struck the ground is the adjacent side (10m), and we are asked to find the length of the hypotenuse (the whole height of the tree).
We can use the cosine of the given angle to solve this problem. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse.
So, cos(30) = adjacent/hypotenuse
We know that cos(30) = √3/2 and the length of the adjacent side is 10m.
So, √3/2 = 10/hypotenuse
Solving for the hypotenuse gives: hypotenuse = 2*10/√3 = 20/√3
To rationalize the denominator, we multiply the numerator and the denominator by √3, which gives us: hypotenuse = 20√3/3
So, the whole height of the tree is 20√3/3 meters.
Therefore, the correct answer is (c) m20 3.
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