Confirm that the triangle in question is a right triangle. In a word, problem it should be noted that one of the triangle's angles measures 90 degrees; if scrutinizing a diagram, a right angle is denoted by a small box at the intersection of two perpendicular lines.
Recall or deduce the formula for sine and write it down: sine(θ) = opp/hyp, where (θ) is the degree of the angle of interest, "opp" is the length of the triangle side opposite to the angle of interest and "hyp" is the length of the hypotenuse.
Determine if there is enough information to solve for the degree of the angle of interest using the sine function. Both the length of the opposite side and the length of the hypotenuse must be provided, otherwise the problem is unsolvable using sine.
Rewrite the equation to solve for the degree of the angle of interest: (θ) = (inverse sine)(opp/hyp). Plug in the values provided for the triangle side lengths into their appropriate places. This is the ratio of sides.
Calculate the degree of the angle with the help of a calculator. Take the inverse sine of the ratio of sides by pressing the "2nd" button, then the "SIN" button and then entering the ratio. Some calculators will not have a "2nd" button but rather a "Shift" button. Consult the calculator instructions to determine which combination of buttons triggers the inverse sine function.
Check if the calculated value is correct by confirming that the ratio of the two sides is equivalent to the sine of the angle degree.