Triangle Equations

Here's a quick reference to triangle equations. You can find out more about Pythagoras' Theorem and solving right (right-angled) triangles here and solving all triangles with trigonometry here.

Sum of The Angles


Angles of a TriangleThe sum of the internal angles of a triangle always add up to 180°.

A + B + C = 180°

Area of a Triangle

Area of a Triangle

The area of a triangle is equal to half the length of the base of a triangle, multipled by its height.

Area = 1/2 base x height

Pythagoras’ Theorem

Hypotenuse Pythagoras’ Theorem is used to find the side lengths of a right triangle

a² + b² = hypotenuse²

Trigonometry for Right Triangles

There are three basic trigonometry rules associated with right triangles:

sinϑ = opposite ÷ hypotenuse

cosϑ = adjacent ÷ hypotenuse

tanϑ = opposite ÷ adjacent

Trigonometry for All Triangles

The Cosine Rule, the Sin Rule and the Tangents Rule can used to solve all triangles.

Cosine Rule

Angle and Side Naming Convention

c² = a² + b² - 2ab(cosC) or

Sine Rule

a ÷ sinA = b ÷ sinB = c ÷ sinC

Tangents Rule

(a - b) ÷ (a+b) = tan(½ (A - B)) ÷ tan(½ (A + B))

Math.Trig User Reviews

"I'm always a bit reluctant to let my children use a calculator instead of using their heads, so I was pleased to see this app has a section showing the trig formulas behind the solution!"

Find Out More About Math.Trig

Math.Trig is a free iPhone and iPad app for solving triangles. Take a closer look here.