question_answer

Some portion of a 20 meters long tree is broken by the wind and the top struck the ground at an angle of\[{{30}^{o}}\]. The height of the point where the tree is broken is  [MNR 1974]

A) 10 m

B) \[(2\sqrt{3}-3)\,20\,\,m\]

C) \[\frac{20}{3}m\]

D) None of these

Correct Answer: C

Solution :

\[H=20=l+h,\,l=\frac{d}{\cos {{30}^{o}}},\,h=d\tan {{30}^{o}}\] \[\therefore \]  \[d=\frac{20}{(\sec {{30}^{o}}+\tan {{30}^{o}})}=\frac{20}{\sqrt{3}}\] and hence \[h=d\tan {{30}^{o}}=\frac{20}{3}m\].