Question

what is the approximate value of k? use the law of sines to find the answer.
2.9 units
3.8 units
5.1 units
6.2 units
law of sines: $\frac{sin(a)}{a} = \frac{sin(b)}{b} = \frac{sin(c)}{c}$

Explanation:

Step1: Find angle at J

Sum of angles in triangle is $180^\circ$.
$\angle J = 180^\circ - 120^\circ - 40^\circ = 20^\circ$

Step2: Apply Law of Sines

Relate side $k$ to known side/angle.
$\frac{k}{\sin(120^\circ)} = \frac{2}{\sin(20^\circ)}$

Step3: Solve for $k$

Rearrange and compute the value.
$k = \frac{2 \times \sin(120^\circ)}{\sin(20^\circ)}$
Calculate $\sin(120^\circ)=\frac{\sqrt{3}}{2}\approx0.8660$, $\sin(20^\circ)\approx0.3420$
$k \approx \frac{2 \times 0.8660}{0.3420} \approx 5.1$

Answer:

5.1 units