Question

the upper part of a tree is broken by the wind and makes an angle of 30° with the ground, The distance from the root of the tree to the point, where the top touches the ground is 5m. Find the height of the tree ​

Answer 1

Given :

• Angle = 30°
• Distance between root to point where it touches ground = 5 m

To find :

• Height of tree

Solution :

Consider a tree of height h and it breaks such that the y length stands upright and x length gets broken to make 30° angle with ground .

From the figure :

Cos 30° = AB/BC

$\tt \dfrac{ \sqrt{3} }{2} = \dfrac{5}{x} \\ \\ \tt x \sqrt{3 } = 5 \times 2 \\ \\ \tt x = \frac{10}{ \sqrt{3} }$

Again , tan 30° = AC / AB

$\tt \dfrac{1}{ \sqrt{3} } = \dfrac{y}{5} \\ \\ \tt y \sqrt{3} = 5 \\ \\ \tt y = \frac{5}{ \sqrt{3} }$

The height h of the tree is given by :

h = x + y

$\tt h = \dfrac{10}{ \sqrt{3} } + \dfrac{5}{ \sqrt{3} } \\ \\ \tt h = \frac{15}{ \sqrt{3} } \\ \\ \tt h = \frac{15}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ \tt h = \frac{15 \sqrt{3} }{3} \\ \\ \tt h = 5 \sqrt{3} \\ \\ \tt h = 5 \times 1.73 \\ \\ \boxed{\tt h = 8.65 \: m}$

Answer 2

Answer:

Given :

Angle = 30°

Distance between root to point where it touches ground = 5 m

To find :

Height of tree

Solution :

Consider a tree of height h and it breaks such that the y length stands upright and x length gets broken to make 30° angle with ground .

From the figure :

Cos 30° = AB/BC

Step-by-step explanation:

Again , tan 30° = AC / AB

The height h of the tree is given by :

h = x + y