question_answer

In a \[\Delta ABC,\]if \[\angle A=115{}^\circ ,\]\[\angle C=20{}^\circ \]and D is s point on BC such that \[AD\bot BC\]and \[BD=7cm,\]then AD is of length                                                                                                              [SSC (CPO) 2013]

A) \[15\,\,cm\]                   

B) \[5\,\,cm\]

C) \[7\,\,cm\]

D) \[10\,\,cm\]

Correct Answer: C

Solution :

In \[\Delta ABC,\]

\[\angle A=115{}^\circ \]

and       \[\angle C=20\]

\[\therefore \]      \[\angle B=180{}^\circ -(115{}^\circ +20{}^\circ )=45{}^\circ \]

Now, in \[\Delta ABD\]

\[\frac{AD}{BD}=\tan 45{}^\circ \]

\[\Rightarrow \]   \[AD=BD=7\,\,cm\]