Determine all the angles of the triangle. If only two are known, calculate the third by subtracting the other two angles from 180, because the sum of all angles in a triangle will equal 180 degrees. The variables A, B, and C will represent each angle.
Complete the first half of the equation by dividing the length of a side by the sine of its corresponding angle (a / sin A). For example, a side with the length of 12 and a corresponding angle of 30 degrees would be represented as (12 / sin 30).
Complete the second half of the equation with the same formula, while leaving the length of this side as a variable. An unknown side with a corresponding angle of 60 degrees would be represented as (b / sin 90).
Form the two elements as an equality formula and solve for the missing variable. The example provided would yield the equation "(12 / sin 30) = (b / sin 90)." Solving the sine values and cross multiplying will result in "12 = (1/2)b." Further solving the variable "b" determines the missing side's length as 24.
Repeat the steps above for the second missing side length, substituting the second half of the equation with the data from the third angle.