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

We know that $\frac{\sin(J)}{KL}=\frac{\sin(L)}{JK}$. Given $JK = 2.3$, $J = 58^{\circ}$, $L=38^{\circ}$. Let $KL = k$. Then $\frac{\sin(58^{\circ})}{k}=\frac{\sin(38^{\circ})}{2.3}$. Cross - multiply gives $k\times\sin(38^{\circ})=2.3\times\sin(58^{\circ})$. So, $k=\frac{2.3\times\sin(58^{\circ})}{\sin(38^{\circ})}$.

Step3: Calculate k

$\sin(58^{\circ})\approx0.848$, $\sin(38^{\circ})\approx0.616$. Then $k=\frac{2.3\times0.848}{0.616}=\frac{1.95}{0.616}\approx3.17\approx3.2$ units.

Answer:

$k\approx3.2$ units, $KL\approx3.2$ units