Question

using the law of sines for the asa case
determine the measures of all unknown angles and side lengths of $\triangle jkl$. round side lengths to the nearest hundredth.
$m\angle k = $
$jk \approx $
$lk \approx $
in $\triangle jkl$, $\angle j=110^\circ$, $\angle l=28^\circ$, $jl=15$

Explanation:

Step1: Calculate $\angle K$

Sum of angles in a triangle is $180^\circ$.
$m\angle K = 180^\circ - 110^\circ - 28^\circ = 42^\circ$

Step2: Find side $JK$ via Law of Sines

Law of Sines: $\frac{JK}{\sin L} = \frac{LJ}{\sin K}$
$JK = \frac{15 \times \sin 28^\circ}{\sin 42^\circ}$
$JK \approx \frac{15 \times 0.4695}{0.6691} \approx 10.43$

Step3: Find side $LK$ via Law of Sines

Law of Sines: $\frac{LK}{\sin J} = \frac{LJ}{\sin K}$
$LK = \frac{15 \times \sin 110^\circ}{\sin 42^\circ}$
$LK \approx \frac{15 \times 0.9397}{0.6691} \approx 20.90$

Answer:

$m\angle K = 42^\circ$
$JK \approx 10.43$
$LK \approx 20.90$