Question

A tree break due to storm and the broken part bends so that the top of the tree touches the ground making an angle ${30}^o$ 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.

Answer 1

The broken part of the tree, the part which is still attached to the ground and the ground forms a right angled triangle ABC in which the broken part AB is the hypotenuse, the stump is BC which is perpendicular to the ground CA.

given CA= 8 m

Now applying the trigonometric functions, we have

$\cos 30=\frac{CA}{AB}$ and $\sin 30=\frac{1}{2}=\frac{BC}{AB}$

we know CA =8m

$\frac{1}{\sqrt{2}}=\frac{8}{AB}$

$AB=8\sqrt{2}m$

so, $\sin 30=\frac{1}{2}=\frac{BC}{AB}=\frac{BC}{8\sqrt{2}}$

$BC=4\sqrt{2}m$

Therefore the height of the tree is AB+BC =$4\sqrt{2}(1+2)m$