Quantitative Aptitude Ques 789

Question: 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

Options:

A) $ 15cm $

B) $ 5cm $

C) $ 7cm $

D) $ 10cm $

Show Answer

Answer:

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=7cm $