Question

Steps pls and the answer is given

Answer 1

Given :

• A tree breaks due to storm.
• The broken part from the top touches the ground making an angle of 30° with ground.
• The distance between foot of tree to the point where the broken bent part touches the ground is 8 m.

To Find :

• Initial Height of the Tree.

Solution :

AC = x m = The portion from where the tree remained unbroken.

CB = y = The broken portion of the tree after the storm.

AB = 8 m = Distance between the foot of the tree and the point where the broken part touches the ground.

Consider Δ ABC.

AC = x m

AB = 8 m.

$\theta$ = 30°

Using,

$\sf{Tan\:\theta\:=\:\dfrac{Opposite\:side\:to\:\angle\:\theta}{Adjacent\:side\:to\:\angle\:\theta}}$

Block in the data,

$\longrightarrow$ $\sf{30\:^\circ\:=\:\dfrac{x}{8}}$

$\longrightarrow$ $\sf{\dfrac{1}{{\sqrt{3}}}=\:\:\dfrac{x}{{8}}}$

$\longrightarrow$ $\sf{8\:=\:\sqrt{3}x}$

$\longrightarrow$ $\sf{\dfrac{8}{{\sqrt{3}}}=x\:\:\:(1)}$

Now, in Δ ABC.

AB = 8 m

CB = y m.

$\sf{\theta\:=\:30\:^\circ}$

Using,

$\sf{Sin\:\theta\:=\:\dfrac{Opposite\:to\:\angle\:\theta}{Hypotenuse}}$

Block in the data,

$\longrightarrow$ $\sf{30^\circ\:=\:\dfrac{x}{y}}$

$\longrightarrow$ $\sf{\dfrac{1}{2}=}$ $\sf{\dfrac{8}{{\sqrt{3}}}}$

$\longrightarrow$ $\sf{\dfrac{1}{2}\:=\:\dfrac{8}{{\sqrt{3}y}}}$

$\longrightarrow$ $\sf{\sqrt{3}y=8\:\times\:2}$

$\longrightarrow$ $\sf{\sqrt{3}y=16}$

$\longrightarrow$ $\sf{y=\dfrac{16}{{\sqrt{3}}}\:\:\:(2)}$

AC = x = 8/√3 m

CD = y = 16/√3 m.

Height of the tree is the sum of AC and CD.

$\longrightarrow$ $\sf{\dfrac{8}{\sqrt{3}}}$ + $\sf{\dfrac{16}{\sqrt{3}}}$

$\longrightarrow$ $\sf{\dfrac{8\:\sqrt{3}+16\:\sqrt{3}}{3}}$

$\longrightarrow$ $\sf{\dfrac{8\:+16\:(\sqrt{3})}{3}}$

$\longrightarrow$ $\sf{\dfrac{24\:\sqrt{3}}{3}}$

$\longrightarrow$ $\sf{\dfrac{\cancel{24}\:\sqrt{3}}{\cancel{3}}}$

$\longrightarrow$ $\sf{8\:\sqrt{3}}$

$\longrightarrow$ $\sf{8\:\times\:1.732}$

$\sf{\big[\sqrt{3}\:=\:1.732\:\big]}$

$\longrightarrow$ $\sf{13.856}$

$\large{\boxed{\sf{\purple{Height\:of\:the\:tree\:=\:AD\:=\:13.856\:m}}}}$