Oblique Triangle Calculator

Background.

School trigonometry is built on right triangles, where SOH-CAH-TOA ties each acute angle to a ratio of two sides. The triangles that turn up outside the classroom rarely oblige. A surveyor sighting a marker across a river, a navigator fixing a position from two bearings, a builder setting out a roof whose two slopes differ — each is working with an oblique triangle, one with no 90° angle at all. There is no hypotenuse, and sine, cosine and tangent no longer link the sides to a single angle in the familiar way.

Two results take over. The law of cosines handles three known sides, or two sides with the angle between them. The law of sines handles the situation here: one side, the angle facing it, and one more angle. Its claim is that every side of a triangle, divided by the sine of the angle across from it, gives the same number. Know one such pair and that shared number is fixed, so any other side is just the shared number times the sine of its own opposite angle.

So from side a, angle A opposite it and a second angle B, the page returns side b, the one facing B, and the remaining angle C, since all three angles must total 180°. To get the third side as well, run it a second time with C in place of B.

Nothing here insists on an obtuse or all-acute shape; if your angles happen to make a right angle at C, the answer is still correct. What the page does not cover is two sides with an angle that is not between them, a case that can have two valid triangles, or a triangle known only by its three sides.

What is oblique triangle calculator?

An oblique triangle is any triangle without a right angle: either all three angles are acute, under 90°, or one is obtuse, over 90°. Solving it means finding the unknown sides and angles from the ones measured. When the known pieces are a side and two angles, the shape and size are fully determined, and the law of sines with the 180° angle sum produces the rest. Here the outputs are side b, opposite angle B, and the third angle C.

How to use this calculator.

1. 01Label the triangle so the side you know is a and the angle across from it — the one corner that side does not touch — is A.
2. 02Enter the other angle you know as B. The page finds the side facing B; for the third side, repeat with C as the target angle.
3. 03If the side you measured runs between the two angles you know, first subtract both angles from 180°. That result is the angle facing your side, and it is the value to enter as A.
4. 04Give a in any length unit and b comes back in the same unit. Angles are in degrees, and A plus B must stay below 180°.

The formula.

b = a × sin(B) ÷ sin(A), and C = 180° − A − B. The first line is the law of sines rearranged. Because a ÷ sin A = b ÷ sin B = c ÷ sin C in every triangle, one side with its opposite angle sets the common ratio, and multiplying that ratio by sin B gives b. The ratio has a geometric meaning: it equals the diameter of the circle passing through all three corners, which is why it is the same for every side. Angles are entered in degrees and converted to radians, by multiplying by π/180, before the sines are taken. The answer is most sensitive when A is small, because sin A sits in the denominator and a slight error in a narrow angle gets magnified. Any pair of angles adding to 180° or more is refused, since the two sides would never meet.

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.