Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30º angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is 6m. Find the height of the tree before falling down.

Answer 1

In rt Δ ABC,

                 $\frac{AB}{BC}$ = tan 30°

                 $\frac{AB}{6} = \frac{1}{\sqrt{3}}$

⇒ AB =$\frac{6}{\sqrt{3}}$      .............(1)

Again, $\frac{AC}{BC}$ = sec 30°

$\frac{AC}{6} =\frac{2}{\sqrt{3}}$

⇒ AC = $\frac{2}{\sqrt{3}} \times 6 = \frac{12}{\sqrt{3}}$    ..............(2)

Height of the tree = AB + AC

                              = $\frac{6}{\sqrt{3}} +\frac{12}{\sqrt{3}} =\frac{18}{\sqrt{3}}$

                              = $\frac{18}{\sqrt{3}} \times\frac{\sqrt{3}}{\sqrt{3}} = 6 \times\sqrt{3} \ m$

Answer 2

Answer:

Step-by-step explanation: