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 8 m. Find the height of the tree.

Using the given instructions, let's draw a figure. Let BD be the broken part of the tree. Where $\angle$D = 30°

CD = 8 m.

The total height of the tree is the sum of BC and BD (BC + BD)

In $∆$BCD,

tan 30° = $\frac{BC}{CD}$

$\Rightarrow$$\frac{1}{\sqrt{3}}$ = $\frac{BC}{8 }$

$\Rightarrow$BC = $\frac{8}{\sqrt{3}}$

Also cos 30° = $\frac{CD}{BD}$

$\Rightarrow$$\frac{\sqrt{3}}{2}$ = $\frac{8}{BD}$

$\Rightarrow$BD = $\frac{16}{\sqrt{3}}$

$\therefore$ The total height of the tree is the sum of BC and BD = $\frac{8}{\sqrt{3}}$ + $\frac{16}{\sqrt{3}}$m 

$=$ $\frac{24}{\sqrt{3}}$X $\frac{\sqrt{3}}{\sqrt{3}}$

$=$ 8$\sqrt{3}$ m is our Answer.