Triangle Side Calculator

Background.

Finding a missing side of a triangle is really three different problems, and the first job is to work out which one you have. If the triangle has a right angle and you know two sides, Pythagoras settles it. If you know two sides and the angle between them, the law of cosines does. If you know one side and two of the angles, the law of sines does — and that is the case solved here.

Two angles fix the triangle's shape, since the third is whatever is left of 180°. One side then fixes its size. The law of sines links the two: in any triangle, each side divided by the sine of the angle facing it gives the same number. Divide the known side a by the sine of its opposite angle A and you have that number, the triangle's scale; multiply it by the sine of another angle B and you have the side facing B.

The word facing carries the weight. Sides take the lower-case letter of the angle across from them, so a sits opposite A and b opposite B, and mixing up that pairing is the usual cause of a wrong answer. If the side you know lies between your two angles, find the angle opposite it first by subtracting the other two from 180°.

Do not expect sides in proportion to the angles. Sides follow the sines, so doubling an angle never doubles the side facing it, although the longest side always faces the largest angle. The page returns side b and the third angle C; run it again with C as the target for the last side.

What is triangle side calculator?

The missing side here is side b of a triangle in which you already know side a, the angle A opposite it, and a second angle B. The law of sines, a/sin A = b/sin B = c/sin C, gives b directly, and the angle sum of 180° gives the third angle C. One side and two angles pin down exactly one triangle, so there is none of the ambiguity that arises when two sides and an angle not between them are known.

How to use this calculator.

1. 01Sketch the triangle and label it: call the side you know a, the angle across from it A, and the angle across from the side you want B.
2. 02If the side you know lies between your two angles, work out A first as 180° minus the two angles you measured.
3. 03Enter a in whatever unit you measured it — metres, feet, centimetres — and both angles in degrees. A and B together must come to less than 180°.
4. 04Read side b, in the same unit as a, and the third angle C. For the third side, run the page again with C entered as the target angle.

The formula.

b = a × sin B ÷ sin A, and C = 180° − A − B. The first line is the law of sines, a/sin A = b/sin B, rearranged for b. The quotient a ÷ sin A is the same for every side of the triangle, so each side is that one constant multiplied by the sine of the angle opposite it. Because the sine rises steeply near 0° and flattens towards 90°, side lengths respond unevenly to angle: raising B from 10° to 20° nearly doubles b, multiplying it by about 1.97, while raising B from 70° to 80° adds only about 5%. The second line is the angle sum of a flat triangle. Angles are converted from degrees to radians before the sines are taken, and any pair of angles that leaves C at zero or below is refused, because no triangle has those angles.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.