Question

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $30^\circ$ with it. The distance between the foot of the tree and the point where the top touches the ground is 8 m. Then the height of the tree is:

• A. $8\sqrt{3}$ meters
• B. $10$ meters
• C. $5\sqrt{2}$ meters
• D. $2$ meters

Hint:

In broken tree problems, form a right triangle and apply trigonometric ratios.

Answer 1

The Correct Option is A

Concept: Use right triangle and trigonometry.
Step 1: Let height of broken part = $h$.
The broken part makes $30^\circ$ with the ground.
Step 2: Use cosine.
\[ \cos 30^\circ = \frac{{base}}{{hypotenuse}} = \frac{8}{h} \] \[ \frac{\sqrt{3}}{2} = \frac{8}{h} \Rightarrow h = \frac{16}{\sqrt{3}} \]
Step 3: Total height.
\[ {Height} = h = \frac{16}{\sqrt{3}} = 8\sqrt{3} \]
Hence, the height of the tree is $8\sqrt{3$ meters.