Law of Sines
Relates sides to opposite angles in any triangle.
Key idea
Relates sides to opposite angles in any triangle.
In depth
a/sin A = b/sin B = c/sin C. It relates sides to the opposite angles in any triangle. Use it when you know two angles and a side (AAS, ASA), or two sides and a non-included angle (SSA).
Worked example
A = 40°, B = 60°, a = 8: b = 8 sin 60°/sin 40° ≈ 10.78.
Formula
Real-world uses
- Solving triangular land plots and navigation problems where two angles and one side are known
Common mistake
Matching a side with the wrong angle; each side pairs with its opposite angle.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Law of Sines?
Relates sides to opposite angles in any triangle. It is a topic at the advanced level in Trigonometry.
What is the formula for Law of Sines?
The key formula is a/sinA = b/sinB = c/sinC.
Where is Law of Sines used in real life?
Real-world examples: Solving triangular land plots and navigation problems where two angles and one side are known.
What should I learn before Law of Sines?
Make sure you are comfortable with Trig Equations with Identities, the previous topic in Trigonometry.
What is a common mistake with Law of Sines?
Matching a side with the wrong angle; each side pairs with its opposite angle.
How can I practise Law of Sines?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Law of Sines?
Move on to Ambiguous Case of Law of Sines next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.