A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Uses the law of sines to calculate unknown angles or sides of a triangle. In order to calculate the unknown values you must know and enter 3 known values.
Some calculation choices are redundent but included anyway for exact letter designations.
To calculate any angle, A, B or C, say B, enter the opposite side b then another angle-side pair such as A and a or C and c. The performed calculations follow the side side angle (SSA) method and only use the law of sines to complete calculations for other unknowns.
To calculate any side, a, b or c, say b, enter the opposite angle B and then another angle-side pair such as A and a or C and c. The performed calculations follow the angle angle side (AAS) method and only use the law of sines to complete calculations for other unknowns.
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
Equations from Law of Sines solving for angles A, B, and C
Equations from Law of Sines solving for sides a, b, and c
Triangle perimeter, P = a + b + c
Triangle semi-perimeter, s = 0.5 * (a + b + c)
Triangle area, K = √[ s*(s-a)*(s-b)*(s-c)]
Radius of inscribed circle in the triangle, r = √[ (s-a)*(s-b)*(s-c) / s ]
Radius of circumscribed circle around triangle, R = (abc) / (4K)
Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 512, 2003.