Question

which measures are accurate regarding triangle jkl? select two options.
□m∠k = 94°
□k≈3.7 units
□k≈4.6 units
□kl≈2.5 units
□kl≈3.2 units
law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find angle K

The sum of angles in a triangle is 180°. So, $m\angle K=180^{\circ}-(58^{\circ} + 38^{\circ})=84^{\circ}$.

Step2: Use the law of sines

The law of sines states $\frac{\sin(J)}{k}=\frac{\sin(L)}{j}$. We know $j = 2.3$, $J=58^{\circ}$, $L = 38^{\circ}$. So, $\frac{\sin(58^{\circ})}{k}=\frac{\sin(38^{\circ})}{2.3}$. Then $k=\frac{2.3\times\sin(58^{\circ})}{\sin(38^{\circ})}$.
Calculating, $\sin(58^{\circ})\approx0.848$, $\sin(38^{\circ})\approx0.616$. So, $k=\frac{2.3\times0.848}{0.616}\approx3.2$.

Step3: Regarding side KL

Side KL is side $k$, and we found $k\approx3.2$ units.

Answer:

$k\approx3.2$ units, so the correct options are:

• $k\approx3.2$ units (equivalent to $KL\approx3.2$ units)

There is no other correct option among the given ones based on our calculations. If we assume $KL$ is side $k$, the only correct option from the list is the one stating $KL\approx3.2$ units.