Question

. 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 8 m. Find the height of the
tree.​

Answer 1

Step-by-step explanation:

. 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 8 m. Find the height of the

tree.

Answer 2

Given :-

Angle made by the tree and ground = 30

Distance between the foot of the tree to the point where the top touches the ground = 8 m

To Find :-

Height of the tree.

Solution :-

(Please refer to the attachment provided for better understanding.)

Let AC be the broken part of the tree.

Angle C = 30°

BC = 8 m

Height of the tree = AB

Total height of the tree = AB + AC

In right ΔABC,

cos 30° = BC/AC

We know that,

cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3  ----(1)

Now also,

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3  ----(2)

According to the question,

Total height of the tree = AB + AC

Substituting them,

= 16/√3 + 8/√3

= 24/√3 = 8√3 m

Therefore, the height of the tree is 8√3 m.