How do you use sine rules to find an unknown length?

sina/A = sinb/B

You need 2 angles and another length to do this.

Let's say you have a triangle with angle 34° opposite to a side of length 5 and an angle of 41° opposite to your unknown side.

Applying a/sin(A) = b/Sin(B)

Substitute values:

a/sin(41°) = 5/sin(34°)

a = 5sin(41°)/sin(34°) (At this point use your calculator to find the value, or use exact values if applicable).

If you're given two angles and a side opposite the unknown angle, then use the angles in a triangle sum to 180° to find the relevant angle.

For example: if you have angles 75° and 46° and you need to use the last angle to solve the equation, then use 180 - 75 - 46 = 59°