question_answer

The top of a broken tree has its top end touching the ground at a distance 15 m from the bottom, the angle made by the broken end with the ground is \[{{30}^{o}}\]. Then length of broken part is

A) \[10\text{ }m\]                        

B)  \[\sqrt{3}\text{ }m\]  

C)         \[5\sqrt{3}\text{ }m\]        

D)         \[10\sqrt{3}\text{ }m\]                      

Correct Answer: D

Solution :

Let the length of broken point (BC) = x.      In \[\Delta \,ABC,\]                                                 \[\cos \,{{30}^{o}}=\frac{15}{x}\]             \[\Rightarrow \]            \[x\times \frac{\sqrt{3}}{2}=15\] \[\Rightarrow \]            \[x=5\sqrt{3}2=10\sqrt{3}\,m\]