Question

A triangle $ABC$ has side $c=2\sqrt{2}$ and $\angle A={30}^0$ lf the radius of its circumcircle is 2, then

• A. $a=2\sqrt{2},C={60}^0$
• B. $a=2,C={45}^0$
• C. $a=2,C={135}^0$
• D. $a=2,C={45}^{0}or{135}^o$

Answer 1

The correct option is D $a=2,C={45}^{0}or{135}^o$

$R=\frac{a}{2sinA}$

$R=\frac{c}{2sinC}$

$2=\frac{a}{2\times \frac{1}{2}}$

$a=2$

$2=\frac{2\sqrt{2}}{2sinC}$

$sinC=\frac{1}{\sqrt{2}}$

$C={45}^0$ or ${135}^0$.