Question

a tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 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

Answer:

h = 8÷root3 m

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hope this helps you ..

Answer 2

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$\large\underline{Given:-}$

• The ground and making angle 30°
• The top touches the ground is 8 m.

$\large\underline{To find:-}$

• find the height of the tree...?

$\large\underline{Solutions:-}$

$\: \: \: \: \: \star \: \: \: In \:\: \triangle \: ABC$

$\: \: \: \: \: \leadsto Cot \: {30} \degree \: \: = \: \: \frac{AB}{AC} \: \: = \: \: \frac{B}{P} \: \: \: \: {(B \: = \: Base, \: \: P \: = \: Perpendicular)}$

$\: \: \: \: \: \leadsto \sqrt{3} \: \: = \: \: \frac{8}{AC}$

$\: \: \: \: \: \leadsto AC \: \: = \: \: \frac{\sqrt{3}}{8}$

$\: \: \: \: \: \therefore x \: \: = \: \: \frac{\sqrt{3}}{8}$

$\: \: \: \: \: \star \: \: \: In \:\: \triangle \: ABC$

$\: \: \: \: \: \leadsto Cos \: {30} \degree \: \: = \: \: \frac{AB}{BC} \: \: = \: \: \frac{B}{H} \: \: \: \: {(B \: = \: Base, \: \: H \: = \: Hypothesis)}$

$\: \: \: \: \: \leadsto \frac{\sqrt{3}}{2} \: \: = \: \: \frac{8}{y}$

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

$\: \: \: \: \: \leadsto y \: \sqrt{3} \: \: = \: \: {16}$

$\: \: \: \: \: \leadsto y \: \: = \: \: \frac{16}{\sqrt{3}}$

$\: \: \: \: \: \star \: \: \: Now, \: \: height \: \: of \: \: the \: \: tree \: \: \leadsto \: \: x \: + \: y$

$\: \: \: \: \: \leadsto \frac{8}{\sqrt{3}} \: + \: \frac{16}{\sqrt{3}}$

$\: \: \: \: \: \leadsto \frac{24}{\sqrt{3}}$

$\: \: \: \: \: \star \: \: \: Now, \: \: Multiplying \: \: by \: \: {24}{\sqrt{3}}$

$\: \: \: \: \: \leadsto \frac{24}{\sqrt{3}} \: \times \: \frac{\sqrt{3}}{\sqrt{3}}$

$\: \: \: \: \: \leadsto \frac{{24} \: \sqrt{3}}{3}$

$\: \: \: \: \: \leadsto \frac{{24} \: \sqrt{3}}{3}$

$\: \: \: \: \: \leadsto {8} \: \sqrt{3}$

»★ Hence,

$\: \: \: \: \: \star \: \: \: The \: \: height \: \: of \: \: the \: \: tree \: \: {8} \: \sqrt{3}.$

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