question_answer

A telegraph post gets broken at a point against a storm, and its top touches the ground at a distance 20 m from the base of the post making an angle 30° with the ground. What is the height of the post?

A) \[\frac{40}{\sqrt{3}}m\]    

B) \[20\sqrt{3}m\]

C) \[40\sqrt{3}m\]  

D) 30m

Correct Answer: B

Solution :

Let MN be the telegraph post and it gets broken at A in such a way that its top M touches the ground and thus makes an angle of 30° with the ground at P. \[\Rightarrow \]   MA = AP In \[\Delta ANP\] \[\tan 30{}^\circ =\frac{AN}{NP}\,\,;\frac{1}{\sqrt{3}}=\frac{AN}{20}\] \[\Rightarrow AN=\frac{20}{\sqrt{3}}m\] Similarly, \[cos\text{ }30{}^\circ =\frac{NP}{AP}\] \[\frac{\sqrt{3}}{2}=\frac{20}{AP}\Rightarrow =\frac{40}{\sqrt{3}}m=MA\] Height of the pole = AN + MA \[\frac{20}{\sqrt{3}}+\frac{40}{\sqrt{3}}=\]