Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 meters. Find the height of the tree.

• A.
  12.5 m
• B.
  20 m
• C.
  17.32 m
• D.
  5.73 m

Answer 1

The correct option is C

17.32 m

Let AC be the height of the tree (before break out) which is (x + h) m
Given, the broken portion of the tree is making an angle of ${30}^{\circ }$ with the ground.

From the fig.
In ΔBCD, we have

$tan{30}^{\circ }=\frac{BC}{DC}$

$\frac{1}{\surd 3}=\frac{h}{10}$

$h=\frac{10}{\surd 3}$

Next, in ΔBCD

$cos{30}^{\circ }=\frac{DC}{BD}$

$\frac{\surd 3}{2}=\frac{10}{x}$

$x=\frac{20}{\surd 3}m$

So,
$x+h=\frac{20}{\surd 3}+\frac{10}{\surd 3}$

$=\frac{30}{\surd 3}$

$=10\surd 3=10\left(1.732\right)=17.32m$

Hence, the height of tree is 17.32 m.