question_answer

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

A) \[15\,\,cm\]                   

B) \[5\,\,cm\] 

C) \[7\,\,cm\]                     

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

Correct Answer: C

Solution :

(c)

Given,   \[\angle A=115{}^\circ \]

\[\angle C=20{}^\circ \]

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

Now, in \[\Delta ABD\]

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

\[\Rightarrow \]   \[AD=BD=7\,\,cm\]        \[[\because tan45{}^\circ =1]\]