A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. The height from the bottom of the tree from where it is broken by the wind is approximately

Question

A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. The height from the bottom of the tree from where it is broken by the wind is approximately (A) 5.57 m (B) 5.21 (C) 5.36 (D) 5.9

Tardigrade Admin · Accepted Answer

sin 60°=(x/12-x) (√3/2)=(x/12-x) 12 √3-√3 x=2 x x(2+√3)=12 √3 x=(12 √3/2+√3) x (2-√3/2-√3) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c15e8e068e9941219e13a610fc47c564-.png" /> x=12(2 √3-3) x=12(2 × 1.732-3) x=12 × 0.464 x=5.568 m

Q. A tree $12 m$ high, is broken by the wind in such a way that its top touches the ground and makes an angle $6 0^{\circ}$ with the ground. The height from the bottom of the tree from where it is broken by the wind is approximately

$5.57 m$

$5.21$

$5.36$

$5.9$

$sin 6 0^{\circ} = \frac{x}{12 - x}$
$\frac{3}{2} = \frac{x}{12 - x}$
$123 - 3 x = 2 x$
$x (2 + 3) = 123$
$x = \frac{12 3}{2 + 3}$ x $\frac{2 - 3}{2 - 3}$

$x = 12 (23 - 3)$
$x = 12 (2 \times 1.732 - 3)$
$x = 12 \times 0.464$
$x = 5.568 m$

Q. A tree 12m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60∘ with the ground. The height from the bottom of the tree from where it is broken by the wind is approximately

5.57m

5.21

5.36

5.9