Question

using the law of sinesdetermine the measures of all unknown angles and side lengths of $\triangle jkl$. round side lengths to the nearest hundredth.$mangle k =$ $$$$jk =$ LXB1lk =$ $$$in $\triangle jkl$, $jl=15$, $mangle j=110^circ$, $mangle l=28^circ$

Explanation:

Step1: Calculate $\angle K$

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

Step2: Find length $JK$ via Law of Sines

Law of Sines: $\frac{JK}{\sin L} = \frac{JL}{\sin K}$
$$JK = \frac{JL \cdot \sin L}{\sin K} = \frac{15 \cdot \sin28^\circ}{\sin42^\circ}$$
Calculate $\sin28^\circ\approx0.4695$, $\sin42^\circ\approx0.6691$:
$$JK \approx \frac{15 \cdot 0.4695}{0.6691} \approx 10.42$$

Step3: Find length $LK$ via Law of Sines

Law of Sines: $\frac{LK}{\sin J} = \frac{JL}{\sin K}$
$$LK = \frac{JL \cdot \sin J}{\sin K} = \frac{15 \cdot \sin110^\circ}{\sin42^\circ}$$
Calculate $\sin110^\circ\approx0.9397$:
$$LK \approx \frac{15 \cdot 0.9397}{0.6691} \approx 20.92$$

Answer:

$m\angle K = 42^\circ$
$JK \approx 10.42$
$LK \approx 20.92$