Write down the Pythagorean theorem. The theorem states that the hypotenuse (longest side of a right triangle opposite from the 90-degree angle) squared is equal to the addition of the square of each of the other two sides or a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides.
Substitute the known length values for the corresponding coefficients. For example, given a hypotenuse length of 5 and another side with a length of 4, we would write 4^2 + b^2 = 5^2.
Solve for the unknown coefficient. In our example, we would solve for the unknown coefficient b using simple algebra, resulting in the length of the unknown side as b=3. A link for help in using the Pythagorean theorem is available in the Resources section.
Determine which trigonometric function should be used and write down its corresponding formula. The basic trigonometric functions are sine, cosine and tangent. A link is provided in the Resources section for information regarding these three functions and example problems. For example, for an unknown side (x) opposite of the known angle, a, of 27 degrees, with a given hypotenuse length of 5, we would use the sine function as sin(a) = (opposite side/hypotenuse).
Substitute known values into the equation. In our example, this would give us sin(27) = x/5
Solve the equation for the unknown using a graphing calculator and algebra. We would do this by obtaining a value for sin(27) from our calculator and subsequently multiplying that by 5, giving us x = sin(27)*5 or x = 2.3.
Determine which trigonometric function should be used based on which side lengths are given and write down its corresponding formula. Let's use the same two values as in the previous problem to see if we get an angle of 27 degrees. So, with a given hypotenuse of 5 and a side opposite of the unknown angle of 2.3, we would need to again use the sine function.
Substitute known values into the equation. In our example, this would give us sin(a) = 2.3/5.
Solve for the unknown angle. To get (a) on one side, we need to take the inverse sin or arcsin function of both sides. Therefore, plugging this into our calculator we get (a) = arcsin( 2.3/5), which equals 27.3 degrees.