What is the formula for Sine Rule (Law of Sines)?

The mathematical formula for Sine Rule (Law of Sines) is a/sin(A) = b/sin(B) = c/sin(C). It is used for finding unknown side lengths or angle measures in any non-right oblique triangle.

What do the variables in the Sine Rule (Law of Sines) formula represent?

In the formula a/sin(A) = b/sin(B) = c/sin(C): a, b, c = Lengths of triangle sides, A, B, C = Angles opposite to sides a, b, c.

How do you calculate Sine Rule (Law of Sines) step-by-step?

To calculate sine rule (law of sines): 1. Identify the given values (a, b, c = Lengths of triangle sides, A, B, C = Angles opposite to sides a, b, c). 2. Substitute the values into the formula a/sin(A) = b/sin(B) = c/sin(C). 3. Simplify and evaluate step-by-step.

PanMaths.comFree Printable Math Formula Reference Sheet

Sine Rule (Law of Sines)

Trigonometry • Grades 9, 10, 11

Trigonometry

Sine Rule (Law of Sines)

Solve any triangle when you know angle-side pairs.

The Formula

a/sin(A) = b/sin(B) = c/sin(C)

Used for: Finding unknown side lengths or angle measures in any non-right oblique triangle

a, b, cLengths of triangle sides

A, B, CAngles opposite to sides a, b, c

⚡Live Interactive Quick Solver

Instant Calculation

Side a:

Angle A (°):

Angle B (°):

Side b (opposite B):5.20 units

b = (3 × sin(60°)) / sin(30°) = 5.20• Angle C = 180° - 30° - 60° = 90°

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

📝 Practice Worksheets→

✨ Free Classroom Assessment ToolSet A & Set B Anti-Cheat

Custom Math Quiz & Test Maker

Need a mixed Friday review or unit assessment? Create a custom test combining multiple math skills in 15 seconds.

✓Anti-cheat Set A & Set B with alternate numbers for adjacent desks
✓100% step-by-step teacher grading keys with intermediate lines
✓1-click Google Classroom links for student tablet/Chromebook testing

✨ Build Custom Worksheet in 15 Seconds →

🎓 100% Free for Teachers & Parents • No Signups Required • Pure Printable PDF

🎯 When to Use the Sine Rule

Best for triangles where you know corresponding angle-side pairs:

📊Works for ANY triangle

Not just right triangles!

🔄Sides match opposite angles

Side a is across from angle A

📐Need 2 known pairs

Use when you know angle + opposite side

📝 Worked Examples

Find a Side

Given: A = 30°, a = 5, B = 60°. Find b.

Set up ratioa/sin(A) = b/sin(B)

Substitute5/sin(30°) = b/sin(60°)

Solveb = 5 × sin(60°)/sin(30°)

Calculateb = 5 × 0.866/0.5 = 8.66

Answer: b ≈ 8.66

Find an Angle

Given: a = 8, A = 40°, b = 10. Find B.

Set up ratiosin(A)/a = sin(B)/b

Solve for sin(B)sin(B) = b × sin(A)/a

Calculatesin(B) = 10 × sin(40°)/8

Inverse sineB = sin⁻¹(0.804) ≈ 53.5°

Answer: B ≈ 53.5°

💡 Pro Tips

Ambiguous case

When finding angles, sin⁻¹ may give two possible answers (acute or obtuse)

Use degrees or radians

Just be consistent! Check your calculator mode.

When to use

Use sine rule when you have angle-side pairs; cosine rule otherwise

Name: _______________________________Date: _______________Class/Period: _________

Related Formulas

📈

TrigonometryCosine Rule (Law of Cosines)

→📐

GeometryPythagorean Theorem

→🌊

TrigonometryTrigonometric Identities

→🔺

GeometryArea of a Triangle

→