Triangle Length Calculator

Background.

In any triangle, the sides are in proportion to the sines of the angles facing them. A side opposite a 60° angle is longer than a side opposite a 30° angle by exactly sin 60° ÷ sin 30°, about 1.732, whether the triangle is drawn on paper or pegged out across a field. That single proportion turns one measured length into every other length, as long as you know the angles.

Finding a missing length starts with knowing which kind of problem you have. In a right triangle, Pythagoras or the basic sine, cosine and tangent ratios do the job. With two sides and the angle between them, the law of cosines gives the third side. With two sides and an angle that is not between them, two different triangles can fit the data, and the problem needs care. The case handled here is the forgiving one: one side and two angles, which always pins down exactly one triangle as long as the angles leave room for a third.

You supply side a, the angle A facing it and a second angle B. The page returns side b, the one facing B, in whatever unit a was measured in, together with the third angle. Angle pairs adding up to 180° or more are refused, because no triangle can contain them.

Most wrong answers come from pairing the known side with the wrong angle. A is not one of the angles touching side a; it is the corner directly across from it. In the example on this page, putting the 60° angle in A instead of the 30° one gives a side of about 2.887 instead of 8.660, out by a factor of three, and nothing else in the output looks amiss.

What is triangle length calculator?

Here a triangle side length means the length of one side worked out from another side and the triangle's angles. The tool is the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C, which holds in every triangle, whether acute, right-angled or obtuse. Given side a and the angles A and B, the unknown side b is fully determined, and the third angle C follows from the fact that the three angles total 180°. One side is solved per run, in any length unit.

How to use this calculator.

1. 01Sketch the triangle and mark the corner directly across from the side you know as A. Enter that side's length in Known side a, in metres, feet or any other unit.
2. 02Enter the angle at that opposite corner in Opposite angle A, in degrees.
3. 03Enter the angle at the corner facing the side you want in Target angle B. If what you measured was an outside angle, subtract it from 180° before entering it.
4. 04Read Solved side b, in the same unit as side a, and the Third angle. For the remaining side, put that third angle into Target angle B and solve once more.

The formula.

b = a × sin B ÷ sin A, and C = 180° − A − B. The first equation is the law of sines, a ÷ sin A = b ÷ sin B, rearranged for b. The ratio sin B ÷ sin A depends only on the two angles, so side b is simply side a multiplied by a fixed scale factor: double the known side and the answer doubles, while changing the angles changes only that factor. Angles are converted from degrees to radians before the sines are taken. Because sin x equals sin(180° − x), an obtuse angle gives the same scale factor as its supplement, but the angle sum still fixes the third angle, so there is never more than one triangle to choose between. Each angle must be greater than 0° and less than 180°, and A plus B must stay below 180°.

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.