Question

In triangle ABC, c = 8, b = 6, and ∠C = 60°. sin∠B = _____

Answer 1

Hello,

sin B/b=sin C/c
==>sin B=√3 / 2 * 6/8=3√3 /8

Answer 2

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, $SinB=0.649^{\circ}$.