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 $30°$with it. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.

Answer 1

Total height of the tree is $=AB+AC$

In Right $∆ABC,$

$$\begin{gathered} BC=8m \\ AB/BC=\tan 30° \\ AB/BC=1/\surd 3 \\ AB=8/\surd 3——-\left(1\right) \end{gathered}$$

Now,

$$\begin{gathered} BC/AC=\cos 30° \\ 8/AC=\surd 3/2 \\ \surd 3AC=16 \\ AC=16/\surd 3——\left(2\right) \end{gathered}$$

From$\left(1\right)$ and $\left(2\right)$

Height of tree $=AB+AC$

$$\begin{gathered} =8/\surd 3\times 16\surd 3 \\ =8\surd 3m \\ 8\times 1.73=13.84m \end{gathered}$$

The height of the tree is $13.84m$.