question_answer

A ladder is resting against a wall at a height of 10m. If the ladder is inclined with the ground at an angle of \[30{}^\circ \], then the distance of foot of the ladder from the wall is

A)  \[\frac{10}{\sqrt{3}}\] m                      

B)  \[\frac{20}{\sqrt{3}}\]m

C)  \[10\sqrt{3}\]m             

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

Correct Answer: C

Solution :

  AB = wall =10 metre \[\angle \]ACB = \[30{}^\circ \] BC=\[x\] metre \[\therefore \] From \[\Delta \]ABC, tan \[30{}^\circ \]=\[\frac{AB}{BC}\]             \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{10}{x}\] \[\Rightarrow \]\[x=10\sqrt{3}\] metre