Uses the law of cosines to calculate unknown sides of a triangle. In order to calculate the unknown values you must enter 3 known values.
Law of Cosines Formula / Calculator
Gamma( γ ) = ?
a = 10
b = 9
c = 3
$$\gamma=cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)$$
$$\gamma=cos^{-1}\left(\frac{10^2+9^2-3^2}{2\ast a\ast b}\right)$$
$$\gamma\approx17.50^{\mathrm o}$$
Gamma( γ ) = 3
a = ?
b = 2
c = 3
$$a=b\ast\cos\gamma\;+\;\sqrt{c^{2\;}\;-\;\;b^2\;\;\ast\;\;\left(\sin\gamma\right)^2}$$
$$a=2\;\ast\;\cos\left(3^\circ\right)\;+\;\sqrt{3^{2\;}\;-\;\;2^2\;\;\ast\;\;\left(\sin\left(3^\circ\right)\right)^2}$$
Gamma( γ ) = 3
a = 4
b = ?
c = 5
$$b=a\;\ast\;\cos\gamma\;+\;\sqrt{c^2\;-\;a^2\;\;\ast\;\left(\sin\gamma\right)^2}$$
$$b=4\;\ast\;\cos\left(171.89\right)\;+\;\sqrt{5^2\;-\;4^2\;\;\ast\;\left(\sin\left(171.89\right)\right)^2}$$
Gamma( γ ) = 3
a = 4
b = 6
c = ?
$$c=\sqrt{a^{2\;}\;+\;\;b^2\;\;-\;\;2\ast a\ast b\;\ast\cos\gamma}$$
$$c=\sqrt{4^{2\;}\;+\;\;6^2\;\;-\;\;2\ast4\ast6\;\ast\cos\left(171.89^\circ\right)}$$