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

$\frac{\sin K}{2.7}=\frac{\sin105^{\circ}}{4.7}$

Step2: Solve for $\sin K$

$\sin K=\frac{2.7\times\sin105^{\circ}}{4.7}$
Since $\sin105^{\circ}=\sin(60^{\circ} + 45^{\circ})=\sin60^{\circ}\cos45^{\circ}+\cos60^{\circ}\sin45^{\circ}=\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2}+\frac{1}{2}\times\frac{\sqrt{2}}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.9659$.
Then $\sin K=\frac{2.7\times0.9659}{4.7}\approx\frac{2.608}{4.7}\approx0.5549$.

Step3: Find angle $K$

$K=\sin^{- 1}(0.5549)\approx34^{\circ}$

Answer:

$34^{\circ}$