Answer:
sin∠B=0.649°
Step-by-step explanation:
Given: In triangle ABC, c = 8, b = 6, and ∠C = 60°.
To find: sin∠B
Solution: using the sine formula that is \(\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}\), we get
\(\frac{SinA}{a}=\frac{SinB}{6}=\frac{Sin60^{\circ}}{8}\)
Taking the second and third equality, we get
\(\frac{SinB}{6}=\frac{Sin60^{\circ}}{8}\)
⇒\(\frac{SinB}{6}=\frac{\frac{\sqrt{3}}{2}}{8}\)
⇒\(\frac{SinB}{6}=\frac{\sqrt{3}}{16}\)
⇒\(SinB=\frac{\sqrt{3}{\times}6}{16}\)
⇒\(SinB=\frac{3\sqrt{3}}{8}\)
⇒\(SinB=0.649^{\circ}\)
Thus, \(SinB=0.649^{\circ}\).
