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13 results for “triangle”

Formulae (13)

a^2 + b^2 = c^2

Relates the sides of a right triangle.

A = \frac{1}{2} b h

Area of a triangle from base and height.

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

Relates sides to opposite angles in any triangle.

c^2 = a^2 + b^2 - 2ab\cos C

Generalizes Pythagoras to any triangle.

A = \sqrt{s(s-a)(s-b)(s-c)}

Area of a triangle from its three sides, s = (a+b+c)/2.

P = a + b + c

Sum of the three sides of a triangle.

R = \frac{abc}{4K}

Radius of a triangle circumscribed circle.

r = \frac{K}{s}

Radius of a triangle inscribed circle.

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

Relates sides of any triangle to the sines of opposite angles.

c^2 = a^2 + b^2 - 2ab\cos C

Generalises Pythagoras to any triangle.

\frac{a-b}{a+b} = \frac{\tan\tfrac{A-B}{2}}{\tan\tfrac{A+B}{2}}

Relates two sides and their opposite angles.

\text{Area} = \tfrac{1}{2}ab\sin C

Area from two sides and the included angle.

\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}

Triangle area from the three side lengths, where s is the semi-perimeter.