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

Answer:

$\pi {r}^{2 } \\ 22 \div 7 \times 8 = 25.14$

Answer 2

Answer:

${}\huge\mathfrak\pink{Required answer}$

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° = BC/AC

We know that, cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3 …(1)

Also,

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3 ….(2)

:• Therefore, total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

$\huge\boxed{\fcolorbox{blue}{orange}{hope it helps}}$