How To Calculate an Angle From Two Sides

By Delia Rollow; Updated April 24, 2017
You can calculate both of the secondary angles in a triangle, as long as one angle is square.

You can use geometric equations to calculate any angle given two sides of a right triangle. To do this, one angle in the triangle must be square, meaning that it equals 90 degrees. You can start by drawing a triangle with one right angle around the existing angle.

Draw straight sides out from the angle you wish to calculate if you do not already have them, so that you can form a measurable triangle.

Use your ruler to measure a short distance from the angle along the adjacent, or bottom side, usually 1 to 2 inches is enough. Mark the end of your measurement and make a note of the side's length.

Use the angle square, or any square angle such as the corner of a book or a piece of paper, to draw a line from your mark to the hypotenuse, or the top side. The bottom of the angle square must lie flat with your adjacent side in order to get the right angle perfectly square.

Measure the length of the side you have just drawn, which is called the opposite side since it is directly opposite the angle you are calculating. Make a note of this length.

Calculate the tangent of your angle on your calculator. This is done by dividing the length of the triangle's opposite side by the adjacent side.

With the tangent number still in your display screen, push the Tan-1 key, which will give you the reference angle to the calculated tangent.

Tip

If you do not have a scientific calculator, you can use a tangent table to look up the angle. Tangent tables usually provide tangents for each whole angle through 45 degrees. If your angle is greater than 45 degrees, you can calculate the measure of the third angle, which when added to the 90 degrees of the right angle and the total subtracted from 180 degrees, will give you the angle of the last corner.

About the Author

Cyclist and organic gardener Delia Rollow has been writing since 2010. She has been published in the "Commonwealth LitMag." Rollow has a Bachelor of Science in environmental studies from Bard College.