Law of sines calculator
In any triangle each side divided by the sine of its opposite angle gives the same number: the diameter of the circumcircle.
Side b
13.472 963 553 3
- Side c
- 15.320 888 862 4
- Angle C
- 80.000 00 degrees
- Circumradius
- 7.778 619 134 3
- Area
- 66.341 394 816 9
- Angles are consistent
- 1
Show the working
- Side a = 10
- Angle A opposite it = 40
- Angle B = 60
- Angle C = 180 - 40 - 60 = 80
- k = 10 / sin(rad(40)) = 15.5572
- Side b = 15.5572 * sin(rad(60)) = 13.473
- Side c = 15.5572 * sin(rad(80)) = 15.3209
- Circumradius = 15.5572 / 2 = 7.778 62
- Area = 10 * 13.473 * sin(rad(80)) / 2 = 66.3414
- Angles are consistent = 80 > 0 ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- a / sin A = b / sin B = c / sin C = 2R