Step by step
The question
Question: find angle B of the triangle with A = 30°, a = 3 and b = 8.
1 Match sides and angles
Side a is across from angle A: we know both.
They are partners.
Side b is across from angle B, the angle we want.
2 Write the law of sines
A side over the sine of its partner angle is the same for every pair.
To find an angle, we flip both sides: the sines on top.
sin B over b = sin A over a.
3 Put the numbers in
Now put the numbers in: b = 8, A = 30° and a = 3.
4 Find sin B
To remove the 8 at the bottom, we multiply by 8.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
8/8 is 1.
So just sin B is left.
So sin B = 8 × sin 30° over 3.
The calculator gives sin 30°: exactly 0.5.
8 times 0.5/3 is about 1.3333.
But the sine of an angle is never more than 1.
Side a is too short to reach the bottom line.
So there is no triangle: no answer.
Let's look back.
First: match sides and angles.
Then: write the law of sines.
Then: put the numbers in.
Last: find sin B.