Multiple choice

A 12 m high tree is broken into two parts. The top of the tree strikes the ground and makes an angle of 60° with the level ground. At what height from the ground did the tree break?

  1. 5.57 m

  2. 6 m

  3. 4.47 m

  4. 8 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let AB represent the tree. Let D be a point from where the tree is broken.

Let BD = x m Then, AD = CD = (12 - x) m In right angle $\triangle$DBC, sin 60° = x/(12-x)                                                                 $\sqrt 3$/2 = x/(12-x) $12\sqrt 3 - \sqrt {3x} = 2x$ (2 + $\sqrt 3$) x = 12$\sqrt 3$  x =$\frac{12\sqrt3}{2+ \sqrt3} \times \frac{2 -\sqrt3}{2- \sqrt3}$                                        x = 24$\sqrt 3$ -36 $\Rightarrow$ x = 24 (1.73) - 36 x = 41.568 - 36 = 5.57 m

Keep practicing — related questions