Question

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

Explanation:

Answer:

First, find the third - angle of the triangle. The sum of angles in a triangle is \(180^{\circ}\), so the third - angle \(J=180^{\circ}-120^{\circ}-40^{\circ}=20^{\circ}\).
By the law of sines, \(\frac{k}{\sin K}=\frac{2}{\sin J}\).
We know that \(K = 120^{\circ}\), \(J = 20^{\circ}\), and the side opposite \(J\) has length \(2\).
So \(k=\frac{2\sin120^{\circ}}{\sin20^{\circ}}\).
\(\sin120^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), \(\sin20^{\circ}\approx0.342\).
\(k=\frac{2\times0.866}{0.342}=\frac{1.732}{0.342}\approx5.1\) units.
C. 5.1 units