---
title: "The Sine Rule"
description: "Use a/sin A = b/sin B in triangles with no right angle to find a missing side or angle, and check whether an obtuse second answer also fits."
canonical: https://lightmysky.com/learn/mathematics/the-sine-rule-mt_cTt_-9KZho
source: https://lightmysky.com/learn/mathematics/the-sine-rule-mt_cTt_-9KZho.md
retrieved: 2026-09-12
---

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# The Sine Rule

Use a/sin A = b/sin B in triangles with no right angle to find a missing side or angle, and check whether an obtuse second answer also fits.

Subject: Mathematics · Area: Geometry · Ages 15 to 16
Page: https://lightmysky.com/learn/mathematics/the-sine-rule-mt_cTt_-9KZho

## Ready when they can

- Pair each side with the angle opposite it before substituting
- Find a missing angle and test whether the obtuse partner also works
- Choose the sine rule when a side and its opposite angle are both known

## Lesson: Pair the side with its angle

Triangles with no right angle defeat Pythagoras, so you need the sine rule: a over sin A equals b over sin B equals c over sin C. Before you substitute anything, pair each side with the angle opposite it. Reach for this rule when a side and its opposite angle are both known.

Finding an angle hides one trap. Sine is shared by supplementary angles, so your calculator hands you the acute one while the diagram may show an obtuse angle. Always test 180 minus the calculator value too: 30 and 150 share a sine, and only the diagram tells you which one fits.

**Example.** Try it: angle A is 30 degrees with opposite side 4 cm, and angle B is 90 degrees. Pair a with A and b with B, then write b over sin 90 equals 4 over sin 30. Since sin 90 is 1 and sin 30 is 0.5, b equals 4 divided by 0.5, which is 8 cm.

**Tip.** When no full side-angle pair exists, put the pen down and switch to the cosine rule instead. And always label the triangle before touching any formula: most lost marks come from pairing a side with its neighbour rather than its opposite.

**Recap.** Pair sides with opposite angles, test the obtuse partner, and switch rules when no pair exists.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Exact Values of Sine, Cosine and Tangent](https://lightmysky.com/learn/mathematics/exact-values-of-sine-cosine-and-tangent-mt_SNJEbXYOrR)

## Opens up

- [Combining a Sine and a Cosine into a Single Wave](https://lightmysky.com/learn/mathematics/combining-a-sine-and-a-cosine-into-a-single-wave-mt_IwQkNDRWyq)
- [Bearing Problems with the Sine and Cosine Rules](https://lightmysky.com/learn/mathematics/bearing-problems-with-the-sine-and-cosine-rules-mt_YQFdU4aiFP)
- [The Cosine Rule](https://lightmysky.com/learn/mathematics/the-cosine-rule-mt_yy73gK5CEP)