Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

In a $\Delta ABC,a=8,b=10$ and $c=12.$ Then $C$ is equal to?

• A. $\frac{A}{2}$
• B. $2A$
• C. $3A$
• D. none of these

Answer 1

The correct option is B $2A$

We know, $\cos C=\frac{a^2+b^2-c^2}{2ab}$

$=\frac{64+100-144}{160}$

$=\frac{20}{160}$

$=\frac{1}{8}$ ...(i)

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$=\frac{100+144-64}{240}$

$=\frac{180}{240}$

$=\frac{3}{4}$ ...(ii)

Now, $\cos 2A=2{\cos }^{2}A-1$

$=\frac{18}{16}-1$

$=\frac{2}{16}$

$=\frac{1}{8}$

$=\cos C$

Hence, $2A=C$.