Answer
See below
Work Step by Step
The sum of the angles of the triangle is $180^\circ$
$$A+B+C=180^\circ\\B=180^\circ-B-C\\B=180^\circ-24^\circ-61^\circ\\B=95^\circ$$
Use the law of sines:
$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{y\sin C}$$
First we obtain: $\frac{a}{\sin A}=\frac{c}{\sin C}\\a=\frac{c}{\sin C}\times\sin A=\frac{43}{\sin 95^\circ}\times\sin 24^\circ\approx 17.56$
Then $\frac{b}{\sin B}=\frac{c}{\sin C}\\b=\frac{c}{\sin C}\times\sin B=\frac{43}{\sin 95^\circ}\times\sin {61}^\circ\approx37.75$
