Question

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

Answer 1

Answer:
sin B = 0.65

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:
$\frac{b}{sin(B)}$ = $\frac{c}{sin(C)}$

$\frac{6}{sin(B)}$ = $\frac{8}{sin(60)}$

sin B = 0.649 which is approximately 0.65

Hope this helps :)

Answer 2

Answer:

$\sin \left(B\right)=\frac{3\sqrt{3}}{8}$

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,

$\frac{a}{\sin A}=\frac{b}{\sin B}= \frac{c}{\sin C}$

Consider the last two ratios, we have,

$\frac{b}{\sin B}= \frac{c}{\sin C}$

Substitute, the value , we have,

c = 8, b = 6, and ∠C = 60°

$\frac{6}{\sin B}= \frac{8}{\sin 60^{\circ}}$

Put $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

we have,

$\frac{6}{\sin \left(B\right)}=\frac{8}{\frac{\sqrt{3}}{2}}$

Simplify, we have,

$\sin \left(B\right)=\frac{3\sqrt{3}}{8}$