Question

what is the approximate measure of angle k? use the law of sines to find the answer. 20° 34° 41° 53° law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Apply law of sines formula

$\frac{\sin L}{j}=\frac{\sin K}{l}$, where $L = 106^{\circ}$, $j = 4.7$, $l=2.7$. So $\frac{\sin106^{\circ}}{4.7}=\frac{\sin K}{2.7}$.

Step2: Solve for $\sin K$

$\sin K=\frac{2.7\times\sin106^{\circ}}{4.7}$. First, $\sin106^{\circ}\approx0.9613$. Then $\sin K=\frac{2.7\times0.9613}{4.7}\approx\frac{2.5955}{4.7}\approx0.5522$.

Step3: Find angle $K$

$K=\sin^{- 1}(0.5522)$. Using a calculator, $K\approx34^{\circ}$.

Answer:

$34^{\circ}$