Question

Triangle J K L is shown. Angle J K L is 120 degrees and angle K L J is 40 degrees. The length of K L is 2 and the length of J L is k. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction What is the approximate value of k? Use the law of sines to find the answer.

Answer 1

5.1

Explanation:

Right on EDU

Answer 2

`k \approx 5$ units`

Explanation:

In Triangle JKL

`\angle K=120^\circ\\\angle L=40^\circ\\KL=2\\JL=k`

We want to determine the approximate value of k using the law of sines.

`\angle J+\angle K+\angle L=180^\circ $ (Sum of angles in a \triangle)\\\angle J+120^\circ+40^\circ=180^\circ \\\angle J=180^\circ-(120^\circ+40^\circ)=20^\circ`

Using Law of Sines

`(k)/(\sin K) =(j)/(\sin J) \\(k)/(\sin 120) =(2)/(\sin 20) \\k=\sin 120 * (2)/(\sin 20)\\k=5.06\\k \approx 5$ units`