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

sin∠B=0.649°

Explanation:

Given: In triangle ABC, c = 8, b = 6, and ∠C = 60°.

To find: sin∠B

Solution: using the sine formula that is
`(SinA)/(a)=(SinB)/(b)=(SinC)/(c)`, we get

`(SinA)/(a)=(SinB)/(6)=(Sin60^(\circ))/(8)`

Taking the second and third equality, we get

`(SinB)/(6)=(Sin60^(\circ))/(8)`

⇒
`(SinB)/(6)=((√(3))/(2))/(8)`

⇒
`(SinB)/(6)=(√(3))/(16)`

⇒
`SinB=\frac{√(3){*}6}{16}`

⇒
`SinB=(3√(3))/(8)`

⇒
`SinB=0.649^(\circ)`

Thus,
`SinB=0.649^(\circ)`.