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

Answer:

$k \approx 5 units$

Step-by-step 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

$\dfrac{k}{\sin K} =\dfrac{j}{\sin J} \\\dfrac{k}{\sin 120} =\dfrac{2}{\sin 20} \\k=\sin 120 \times \dfrac{2}{\sin 20}\\k=5.06\\k \approx 5 units$

Answer 2

Answer:

5.1

Step-by-step explanation:

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