Question

law of sines
triangle diagram: vertices j, k, l; angle at k is 120°, angle at l is 40°, side kl = 2, side jl = k
law of sines: \\(\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}\\)
what is the approximate value of \\(k\\)? use the law of sines to find the answer.
5.1 units
3.8 units
2.9 units

Explanation:

Step1: Find angle at J

The sum of angles in a triangle is \(180^\circ\). So, \(\angle J = 180^\circ - 120^\circ - 40^\circ = 20^\circ\).

Step2: Apply Law of Sines

Law of Sines: \(\frac{k}{\sin K}=\frac{KL}{\sin J}\). Here, \(KL = 2\), \(\angle K = 120^\circ\), \(\angle J = 20^\circ\). So, \(\frac{k}{\sin 120^\circ}=\frac{2}{\sin 20^\circ}\).

Step3: Solve for k

\(k=\frac{2\times\sin 120^\circ}{\sin 20^\circ}\). Calculate \(\sin 120^\circ=\frac{\sqrt{3}}{2}\approx0.866\), \(\sin 20^\circ\approx0.342\). Then \(k=\frac{2\times0.866}{0.342}\approx\frac{1.732}{0.342}\approx5.1\).

Answer:

5.1 units