1. ## Trigonometry problem.

The top of the tree, is broken and the broken part bends in such a way that its top makes an angel of $30^o$ with the ground.The distance of the point at which the top of broken tree touches the ground from the root of the tree is 40 meter.Find the height of the tree.

Plz solve this question.

2. Originally Posted by prashantvrm
The top of the tree, is broken and the broken part bends in such a way that its top makes an angel of $30^o$ with the ground.The distance of the point at which the top of broken tree touches the ground from the root of the tree is 40 meter.Find the height of the tree.

Plz solve this question.
Draw yourself a nice figure in which you can show that:

$\tan30=\frac{x}{40}$

$x=40\tan30\approx\boxed{23.1}$

x represents the height of the tree after the break.

Of course, you may have to add the length of the hypotenuse to discover the original height of the tree before the break.

To do this, let h = the hypotenuse or the broken part of the tree.

$\cos30=\frac{40}{h}$

$h \cos 30 = 40 \Longrightarrow h=\frac{40}{\cos 30} \Longrightarrow h \approx \boxed{46.2}$ m.

Original height of the tree: $23.1m+46.2m=\boxed{69.3}$ m.

3. Hi,

When the tree broken and it falls down on the ground, so it makes in the right angle form.
base distance from the root level is 40m
and slant of the tree is hypotenuous that is broken tree which make an angle 30 degree, so u need to find the height of the tree.
use the formula for tan theta