Question

law of sines: \\(\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}\\)\
which measures are accurate regarding triangle jkl? select two options.\
\\(\square m\angle k = 94^\circ\\)\
\\(\square k \approx 3.7\\) units\
\\(\square k \approx 4.6\\) units\
\\(\square kl \approx 2.5\\) units\
\\(\square kl \approx 3.2\\) units

Explanation:

Step1: Calculate $\angle K$

The sum of angles in a triangle is $180^\circ$.
$m\angle K = 180^\circ - 58^\circ - 38^\circ = 84^\circ$

Step2: Solve for side $k$ (JL)

Apply Law of Sines: $\frac{k}{\sin(\angle K)} = \frac{JK}{\sin(\angle L)}$
Substitute values: $k = \frac{2.3 \times \sin(84^\circ)}{\sin(38^\circ)}$
Calculate: $k \approx \frac{2.3 \times 0.9945}{0.6157} \approx 3.7$ units

Step3: Solve for side KL

Apply Law of Sines: $\frac{KL}{\sin(\angle J)} = \frac{JK}{\sin(\angle L)}$
Substitute values: $KL = \frac{2.3 \times \sin(58^\circ)}{\sin(38^\circ)}$
Calculate: $KL \approx \frac{2.3 \times 0.8480}{0.6157} \approx 3.2$ units

Answer:

$\square k \approx 3.7$ units
$\square$ KL $\approx 3.2$ units