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, $m\angle K=180-(58 + 38)=84^{\circ}$.

Step2: Use the law of sines

We know that $\frac{\sin J}{KL}=\frac{\sin L}{JK}=\frac{\sin K}{JL}$. Given $JK = 2.3$, $\angle J=58^{\circ}$, $\angle L = 38^{\circ}$, $\angle K=84^{\circ}$. Using $\frac{\sin J}{KL}=\frac{\sin L}{JK}$, we have $\frac{\sin58^{\circ}}{KL}=\frac{\sin38^{\circ}}{2.3}$. Then $KL=\frac{2.3\times\sin58^{\circ}}{\sin38^{\circ}}$.
$\sin58^{\circ}\approx0.848$, $\sin38^{\circ}\approx0.616$. So $KL=\frac{2.3\times0.848}{0.616}\approx3.2$ units. Also, using $\frac{\sin K}{JL}=\frac{\sin L}{JK}$, $\frac{\sin84^{\circ}}{JL}=\frac{\sin38^{\circ}}{2.3}$, $\sin84^{\circ}\approx0.995$, then $JL=\frac{2.3\times\sin84^{\circ}}{\sin38^{\circ}}=\frac{2.3\times0.995}{0.616}\approx3.7$ units.

Answer:

B. $k\approx3.7$ units
E. $KL\approx3.2$ units