Question

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

sin∠B = _____

Answer 1

`\sin \left(B\right)=(3√(3))/(8)`

Step-by-step explanation:

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

We have to find the value of
`\sin B`

Consider the given triangle ABC,

LAWS OF SINE : States that for a given triangle AbC, with a, b, c and Side a faces angle A,side b faces angle B and side c faces angle C.

We have,

`(a)/(\sin A)=(b)/(\sin B)= (c)/(\sin C)`

Consider the last two ratios, we have,

`(b)/(\sin B)= (c)/(\sin C)`

Substitute, the value , we have,

c = 8, b = 6, and ∠C = 60°

`(6)/(\sin B)= (8)/(\sin 60^(\circ))`

Put
`\sin \left(60^(\circ \:)\right)=(√(3))/(2)`

we have,

`(6)/(\sin \left(B\right))=(8)/((√(3))/(2))`

Simplify, we have,

`\sin \left(B\right)=(3√(3))/(8)`

Answer 2

Answer:
sin B = 0.65

Step-by-step explanation:
To solve this question, we will need to use the sine law that is shown in the attached image.

Here, we have:
c = 8
b = 6
angle C = 60°

Therefore:

`(b)/(sin(B))` =
`(c)/(sin(C))`


`(6)/(sin(B))` =
`(8)/(sin(60))`

sin B = 0.649 which is approximately 0.65

Hope this helps :)