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.

Asked by Abhisek | 1 year ago |  61

##### Solution :-

Using given instructions, draw a figure.

Let AC be the broken part of the tree. Angle C = 30°

BC = 8 m

To Find: Height of the tree, which is AB

From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC

In right ΔABC,

Using Cosine and tangent angles,

cos 30° = $$\dfrac{BC}{AC}$$

We know that, cos 30° = $$\dfrac{\sqrt{3}}{2}$$

$$\dfrac{\sqrt{3}}{2}$$ = $$\dfrac{8}{AC}$$

AC = $$\dfrac{16}{\sqrt{3}}$$ …(1)

Also,

tan 30° = $$\dfrac{AB}{BC}$$

$$\dfrac{1}{\sqrt{3}}$$ = $$\dfrac{AB}{8}$$

AB = $$8\sqrt{3}$$ ….(2)

Therefore, total height of the tree = AB + AC

$$16\sqrt{3} + 8\sqrt{3} = 24\sqrt{3} = 8\sqrt{3}\; m$$

Answered by Pragya Singh | 1 year ago

### Related Questions

#### A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60°

A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

#### A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground

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 from the foot of the tree to the point where the top touches the ground is 10 meters. Find the height of the tree.

#### The length of the shadow of a tower standing on level plane is found to be 2x meters

The length of the shadow of a tower standing on level plane is found to be 2x meters longer when the sun’s attitude is 30° than when it was 30°. Prove that the height of tower is $$x(\sqrt{3}+1)$$ meters.