Question

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

sin∠B = _____

Answer 1

Use the law of sines.

\(\dfrac{b}{\sin B} = \dfrac{c}{\sin C} \)

Answer 2

57.4823 =57.4823?? @mathstudent55

Answer 3

my answer has to be one of these how would I make it to that? @mathstudent55

Answer 4

So setting up the law of sines we have

\[\large \frac{b}{sin(B)} = \frac{c}{sin(C)}\]

We plug in what we know

\[\large \frac{6}{sin(B)} = \frac{8}{sin(60^\circ)}\]

And we want to solve for sin(B)

Answer 5

So first, we can replace sin(60) with what it equals...\(\large sin(60) = \frac{\sqrt{3}}{2}\)

So

\[\large \frac{6}{sin(B)} = \frac{8}{\frac{\sqrt{3}}{2}}\]

Answer 6

Now just cross multiply and solve for sin(B)

Answer 7

The question asks what the sine of angle B is, not what the measure of angle B is.