Triangles And Properties Of Triangle Question 44
Question: In a $ \Delta ABC $ , if $ \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}, $ and the side $ a=2, $ then area of the triangle is
Options:
A) 1
B) 2
C) $ \frac{\sqrt{3}}{2} $
D) $ \sqrt{3} $
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Answer:
Correct Answer: D
Solution:
[d] $ \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c} $
$ \Rightarrow \frac{\cos A}{2R\sin A}=\frac{\cos B}{2R\sin B}=\frac{\cos C}{2R\sin C} $
$ \Rightarrow \cot A=\cot B=\cot C $
$ \Rightarrow A=B=C=60{}^\circ \Rightarrow \Delta ABC $ is equilateral Hence, $ \Delta =\frac{\sqrt{3}}{4}a^{2}=\sqrt{3}. $
BETA
