Question

The upper part of a tree, broken over by the wind, makes an angle of 45° with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. What was the height of the tree before it was broken?

Answer 1

Let the height of the tree after bracking be h m

Here θ = 45°

∴ ${\displaystyle {\tan 45}^{\circ }=\frac{h}{15}}$

${\displaystyle \Rightarrow 1=\frac{h}{15}}$

∴ h = 15 m

Now, length of the tree broken by the wind

= ${\displaystyle \frac{15}{{\sin 45}^{\circ }}}$

= ${\displaystyle 15\sqrt{2}}$

= 21.21 m

So, height of the tree before it was broken is (15 + 21.21) m = 36.21 m.