Question

Solve it quickly ❗❗


Plz​

Answer 1

so u answer is 8√3m

I hope it help u

Answer 2

$\underline{\underline{\LARGE\sf \orange{Given:}}}$

• The broken part of Tree touches the ground and making an angle of 30°.

• The distance between the foot of the tree to the point where the top touches the ground is 8 m.

$\underline{\underline{\LARGE\sf \orange{Find:}}}$

• What is the height of the Tree

$\underline{\underline{\LARGE\sf \orange{Solution:}}}$

In $\triangle$ ABC

$\sf \to\dfrac{AB}{BC}= \dfrac{P}{B} = \tan {30}^{ \circ}$

$\sf \to\dfrac{AB}{8}= \dfrac{1}{ \sqrt{3} }$

Do, cross Multiplication

$\sf \to AB \sqrt{3} = 8$

$\sf \to AB = \dfrac{8}{ \sqrt{3} } m.....(1)$

Now,

$\sf \to\dfrac{AC}{BC}= \dfrac{H}{B} = \sec {30}^{ \circ}$

$\sf \to\dfrac{AC}{8}= \dfrac{2}{ \sqrt{3} }$

Do, cross Multiplication again

$\sf \to AC\sqrt{3} = 8 \times 2$

$\sf \to AC\sqrt{3} = 16$

$\sf \to AC = \dfrac{16}{ \sqrt{3} } m$

Rationalise this

$\sf \to AC = \dfrac{16}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

$\sf \to AC = \dfrac{16 \sqrt{3} }{3} m$

As, it is given that tree breaks due to the storm So, Total Length of the Tree is

$\sf\implies AB + AC = \dfrac{8 \sqrt{3} }{3} + \dfrac{16 \sqrt{3} }{3}$

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

$\sf\implies \dfrac{24\sqrt{3} }{3}$

$\sf\implies \dfrac{24\sqrt{3} }{3} = 8 \sqrt{3} m$

$\underline{\small{ \sf\therefore total \: height \: of \: the \: tree \: is \: 8 \sqrt{3}m}}$