Triangles And Properties Of Triangle Question 21
Question: In a $ \Delta ABC; $ if $ 2\Delta =a^{2}-{{(b-c)}^{2}} $ then value of $ \tan A= $
Options:
A) $ -\frac{4}{3} $
B) $ \frac{4}{3} $
C) $ \frac{8}{15} $
D) $ \frac{4}{15} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ 2\Delta =(a-b+c)(a+b+c) $
$ \Rightarrow 2\Delta =4(s-b)(s-c) $
$ \Rightarrow 2=\sqrt{\frac{s(s-a)}{(s-b)(s-c)}}\Rightarrow \tan \frac{A}{2}=\frac{1}{2} $
$ \therefore \tan A=\frac{2\times \frac{1}{2}}{1-\frac{1}{4}}=\frac{4}{3} $
BETA
