question_answer

Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of \[30{}^\circ \] with the ground. If the length of the broken part is 20 metres, then the remaining part of the tree is of length

A) \[20\text{ }meters\]

B) \[10\sqrt{3}\text{ }meters\]

C) \[10\text{ }meters\]

D) \[10\sqrt{2}\text{ }meters\]

Correct Answer: C

Solution :

  Let \[AB=x\text{ }m\] be the remaining part of the broken tree AC,                              From right angled \[\Delta \,ABC,\]                 \[\sin \,{{30}^{o}}=\frac{AB}{BC}\] or            \[\frac{1}{2}=\frac{x}{20}\] \[\therefore \]  \[x=10m\]