**Laws of Cosines and Sines for Angles/Sides of Triangles
Enter two angles and any side, or 3 sides, or two sides and angle between them, into the boxes
above to get the other sides and angles using the laws of cosines or sines and sum of angles of triangle.
After entering sides/angles click button [Calculate].
**

JavaScript © 2000 by John A. Byers

Law of Cosines:

(side a) = SQRT((side b)^{2} + (side c)^{2} - 2(side b)(side c)cos(angle A))

(side b) = SQRT((side a)^{2} + (side c)^{2} - 2(side a)(side c)cos(angle B))

(side c) = SQRT((side a)^{2} + (side b)^{2} - 2(side a)(side b)cos(angle C))

Solving for the angles from equations above:

(angle A) = arccos [(-(side a)^{2} + (side b)^{2} + (side c)^{2})/(2(side a)(side b))]

(angle B) = arccos [(-(side b)^{2} + (side a)^{2} + (side c)^{2})/(2(side a)(side c))]

(angle C) = arccos [(-(side c)^{2} + (side a)^{2} + (side b)^{2})/(2(side a)(side b))]

where:

arccos [] = arctan(SQRT(1 - X^{2})/X), where X = cos []

Law of Sines:

(side a)/sin(angle A) = (side b)/sin(angle B) = (side c)/sin(angle C)

Law of angular sum of triangle:

(angle A) + (angle B) + (angle C) = 180

To convert degrees to radians (which are used in the formulas):

degrees = radians(180/3.141593)

radians = degrees(3.141593/180)
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