Question

If $sin(B+C)=\frac{\sqrt{3}}{2}$ and$sinA=\frac{1}{2}$, find $B+C$and$A$.

• A. $B+C={60}^{\circ }andA={30}^{\circ }$
• B. $B+C={30}^{\circ }andA={30}^{\circ }$
• C. $B+C={45}^{\circ }andA={60}^{\circ }$
• D. $B+C={60}^{\circ }andA={60}^{\circ }$

Answer 1

The correct option is A $B+C={60}^{\circ }andA={30}^{\circ }$

Trigonometric angles for some specific sine acute angles are given below,
$\begin{array}{cccccc}\theta & 0^{\circ }& {30}^{\circ }& {45}^{\circ }& {60}^{\circ }& {90}^{\circ }\\ Sin\theta & 0& \frac{1}{2}& \frac{1}{\sqrt{2}}& \frac{\sqrt{3}}{2}& 1\end{array}$

From the above table we can see that $B+C={60}^{\circ }$ and $A={30}^{\circ }$