How to Figure the Length of a Side of a Triangle From a Given Angle

Updated April 17, 2017

A triangle is a three-sided two-dimensional figure that consists of a long side connected to two shorter sides. Trigonometric functions such as sine, cosine and tangent can be used to calculate the sides of a triangle given an angle. So, if you are given an angle and the length of one side, there are formulas that allow you to find the length of another side.

Label the angles and sides of the triangle with the dimensions that are given. To calculate the length of a triangle's side given an angle, you will need the length of one other side. If you are not given one angle and the length of at least one side, then the problem cannot be done.

Determine what side of the triangle (hypotenuse, opposite or adjacent side) you need to find. The hypotenuse is the longest side of a triangle. Depending on the angle given, label the opposite side across from the given angle and label the adjacent side as the one that lies next to the angle on either side.

Determine the appropriate trigonometric relationship to use to figure the length of a side of the triangle depending on the information already given. For example, if you have a triangle with an angle given at 53 degrees and a hypotenuse of 8 centimetres, then sine of 53 degrees would equal the opposite side / 8cm. Use a calculator with trigonometric functions or a table of trigonometric function value to look up the sine of 53 degrees. Since the sine of 53 degrees is 0.80, cross-multiplying would yield 0.80 times 8cm or 6.4cm for the length of the opposite side.


Visit the CalculatorSoup website to use a trigonometric functions calculator.

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About the Author

Patricia Smith Michaels has been writing business and technology articles online since 2010. She has written instructional manuals and white papers for corporations and has more than 20 years of experience as a researcher and consultant in the areas of health care, education and management. She holds a Master of Business Administration in management and a Bachelor of Science in computers from St. John's University.