Question

using the law of sines for the asa case. determine the measures of all unknown angles and side lengths of △jkl. round side lengths to the nearest hundredth. m∠k = jk = lk =

Explanation:

Step1: Find angle $K$

The sum of angles in a triangle is $180^{\circ}$. So $m\angle K=180^{\circ}-(110^{\circ} + 28^{\circ})=42^{\circ}$

Step2: Use the Law of Sines to find $JK$

The Law of Sines states $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. We know $JL = 15$, $\angle L=28^{\circ}$, $\angle K = 42^{\circ}$. So $\frac{JK}{\sin L}=\frac{JL}{\sin K}$, then $JK=\frac{JL\sin L}{\sin K}=\frac{15\sin28^{\circ}}{\sin42^{\circ}}\approx10.52$

Step3: Use the Law of Sines to find $LK$

Using the Law of Sines $\frac{LK}{\sin J}=\frac{JL}{\sin K}$, with $J = 110^{\circ}$, $JL = 15$, $K=42^{\circ}$. So $LK=\frac{JL\sin J}{\sin K}=\frac{15\sin110^{\circ}}{\sin42^{\circ}}\approx20.78$

Answer:

$m\angle K = 42^{\circ}$
$JK\approx10.52$
$LK\approx20.78$