what is the approximate value of k? use the law of sines to find the answer. law of sines…

Answer:

C. 3.8 units

Explanation:

Step1: Find angle J

In a triangle, the sum of interior angles is 180°. So, $\angle J=180^{\circ}-120^{\circ}-40^{\circ}=20^{\circ}$.

Step2: Apply the law of sines

According to the law of sines $\frac{\sin(J)}{2}=\frac{\sin(L)}{k}$. We know $\sin(J)=\sin(20^{\circ})\approx0.342$, $\sin(L)=\sin(40^{\circ})\approx0.643$. Substituting the values into the law - of - sines formula: $\frac{0.342}{2}=\frac{0.643}{k}$.

Step3: Solve for k

Cross - multiply to get $0.342k = 2\times0.643$. Then $k=\frac{2\times0.643}{0.342}=\frac{1.286}{0.342}\approx3.8$.