Trigonometry

Law of Sines

Formula

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

What is Law of Sines?

The Law of Sines states that the ratio of each side of a triangle to the sine of its opposite angle is constant. It is useful for solving non-right triangles.

Variables

a
a, b, c — Sides of the triangle
A
A, B, C — Angles opposite to sides a, b, c respectively

Worked Examples

Example 1

In triangle ABC, a = 10, A = 30°, and B = 45°. Find side b.

Solution:

b/sin(45°) = 10/sin(30°). b = 10 × sin(45°) / sin(30°) = 10 × 0.707 / 0.5 ≈ 14.14

Frequently Asked Questions

Related Formulas

Trigonometric Ratios (sin, cos, tan)

sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent

c² = a² + b² − 2ab × cos(C)

Pythagorean Trigonometric Identities

sin²θ + cos²θ = 1

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