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 between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Let AB be the tree of height h. And the top of tree makes an angle 30° with ground. The distance between foot of tree to the point where the top touches is 8m. Let. And
.
Here we have to find height of tree.
So we trigonometric ratios
$\Rightarrow \quad \tan C=\frac{A B}{B C}$
$\Rightarrow \quad \tan 30^{\circ}=\frac{A B}{B C}$
$\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{8}$
$\Rightarrow \quad h=\frac{8}{\sqrt{3}}$
Now in triangle ABC
$\sin 30^{\circ}=\frac{A B}{A C}$
$\Rightarrow \quad \frac{1}{2}=\frac{h}{A C}$
$\Rightarrow \quad \frac{1}{2}=\frac{\frac{8}{\sqrt{3}}}{A C}$
$\Rightarrow \quad A C=\frac{16}{\sqrt{3}}$
So the height of the tree is
$h+A C=\frac{8}{\sqrt{3}}+\frac{16}{\sqrt{3}}$
$=8 \sqrt{3}$
Hence the height of tree is $\mathrm{m}$.
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