Triangle Formula Sheet

These flashcards cover key formulas and concepts related to triangles, including area calculations, radius relationships, and important trigonometric identities.

Semi-perimeter

s = (a + b + c) / 2

Area of a triangle

Delta = 1/2 * base * height

Area using sine

Delta = 1/2 bc sin A (where A is the included angle)

Heron's formula for area

Delta = sqrt[s(s-a)(s-b)(s-c)]

Inradius

r = Delta / s (where Delta is the area and s is the semi-perimeter)

Exradius r1

r1 = Delta / (s-a)

Exradius r2

r2 = Delta / (s-b)

Exradius r3

r3 = Delta / (s-c)

Circumradius

R = abc / (4 Delta) (where a, b, c are the sides of the triangle)

Sine Rule

a/sin A = b/sin B = c/sin C = 2R

Cosine Rule

a^2 = b^2 + c^2 - 2bc cos A

Half-Angle Formula for sine

sin(A/2) = sqrt[(s-b)(s-c)/bc]

Identity for sine and cosine

sin^2 theta = 1 - cos^2 theta

Combined result involving radii

r1 + r2 + r3 - r = 4R