question_answer

In \[\Delta ABC,\] 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

A)  15 cm

B)         5 cm

C)  7 cm   

D)  10 cm

Correct Answer: C

Solution :

In \[\Delta ABC,\angle A=115{}^\circ ,\angle C=20{}^\circ \] \[\therefore \]      \[\angle B=180{}^\circ -(115{}^\circ +20{}^\circ )=45{}^\circ \] Now, In \[\Delta ABD\frac{AD}{BD}=\tan 45{}^\circ \] \[\Rightarrow \]   \[AD=BD=7\,\,cm\]