Question

43 do
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 8m. Find the height of the tree.​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Tree PQ broken at R

$\fbox{So\;Q\;touches\;the\;ground\;at\;S}$

QR = RS

∠PSR = 30°

PS = 8 m

In triangle PSR

$\tt{\rightarrow\dfrac{PR}{PS}=tan30}$

$\tt{\rightarrow\dfrac{PR}{PS}=\dfrac{1}{\sqrt{3}}}$

$\tt{\rightarrow PR=(PS)\dfrac{1}{\sqrt{3}}}$

$\tt{\rightarrow PR=8\dfrac{1}{\sqrt{3}}}$

$\tt{\rightarrow PR=\dfrac{8\sqrt{3}}{3}m}$

Also

$\tt{\rightarrow\dfrac{PS}{RS}=cos30}$

$\tt{\rightarrow\dfrac{PS}{RS}=\dfrac{\sqrt {3}}{2}}$

$\tt{\rightarrow RS=\dfrac{2}{\sqrt{3}}PS}$

$\tt{\rightarrow RS=\dfrac{2}{\sqrt{3}}(8)}$

$\tt{\rightarrow RS=\dfrac{16\sqrt{3}}{3}}$

Height of tree :-

PR + QR = PR + RS

$\tt{\rightarrow=\dfrac{8\sqrt{3}}{3}+\dfrac{16\sqrt{3}}{3}}$

$\tt{\rightarrow\dfrac{24\sqrt{3}}{3}}$

= 8√3 m

Answer 2

${\textbf{Answer}}$