Obtain the proper information to make the calculation. Sketch the right triangle and label the sides --- hypotenuse, adjacent and opposite --- in metric units. Insert the angles in degrees if the question contains information, or use variable (X) to label an unknown angle. Write the values for each side; ensure that they are in the same metric units.
Calculate one side when two sides are given. Calculate the length of a side using the Theorem of Pythagoras, which states that in a right triangle, the square of the hypotenuse is the sum of the squares of the other two sides. To calculate a length of hypotenuse side, calculate opposite length squared plus adjacent length squared, then calculate the square root of the result with the aid of a calculator. To determine the adjacent length, calculate hypotenuse length squared minus opposite length squared, then calculate the square root of the result on a calculator. The calculation of opposite length is similar to the method used to calculate adjacent length. The metric unit of your calculated length is the same as those of the given lengths.
Calculate an angle when two sides are given. Calculate required angle (X) using right triangle trigonometric functions. Identify the two given sides, then choose the appropriate trigonometric function: sine of "X" equals opposite side divided by hypotenuse, tangent of "X" equals opposite side divided by adjacent and cosine of "X" equals adjacent side divided by hypotenuse. For example, if using sine of "X," calculate opposite side divided by hypotenuse with a calculator to obtain a real number. Then take the inverse of sine function (arc sine) of the real number by using a calculator. The result is the measure of the required angle in degrees.
Calculate one side when a side and angle are given. Use the unknown-side label, known-side label and known angle; identity the appropriate trigonometric function relating all three parameters. If the function is tangent, for example, and the unknown label is opposite, calculate the tangent of the angle with a calculator to obtain a real number. Multiply the real number by the adjacent length. The result is the length of the opposite side, and it has the same unit as the adjacent side.
Calculate an angle when two angles are given. The sum of angles in a triangle is 180 degrees. Calculate known angle plus known angle. Subtract the result from 180 degrees.