# find the length of QR

The area of the $$\triangle PQR$$ is equal to $$48.21cm^2$$ if $$PR = 15cm$$ and $$\angle PRQ = 40°$$

I know we use the sine rule by how do we use it wit 1 angle and one side?

What I did is $$15\sin(40) ÷ 48.21 = 0.1999$$

$$\sin^{-1} (0.1999) = 11.53$$

My answer booklet said the answer is $$10$$

How did they get this answer?

You can get two equations: $$A=\frac{pr}{2}\sin(40^{\circ})$$ and $$15^2=p^2+r^2-2pr\cos(40^{\circ})=p^2+r^2-4A\cot(40^{\circ})$$(Note that $$pr=\frac{2A}{\sin(40^{\circ})}$$). With these equations you can compute $$p=RQ$$ or $$r=PQ$$.