Page Description Equation
107 Law of Cosines. SAS. $x,y,z$ are sides of any triangle and $Z$ is the angle between sides $x$ and $y$ and opposite $z.$ Use this form to solve for $z$ when $x,y,Z$ are known. \[ z^2=x^2+y^2-2xy\cos{Z} \]
108 Law of Cosines. SSS. $x,y,z$ are sides of any triangle and $Z$ is the angle between sides $x$ and $y$ and opposite $z.$ Use this form to find the angle $Z$ when the three sides of the triangle are known. Use the $\mathrm{arccos}$ function. \[ \cos{Z}=\frac{x^2+y^2-z^2}{2xy} \]
113 Law of Sines, General Form. $x,y$ are any two sides of any triangle and $X,Y$ are angles opposite those sides \[ \frac{\sin{X}}{x}=\frac{\sin{Y}}{y} \]
114 Law of Sines. SAA, ASA. $x,y$ are any two sides of any triangle and $X,Y$ are angles opposite those sides. Use this form to solve for $x$ when $X,Y,y$ are known. For ASA, find the third angle then treat like SAA. \[ x=\frac{y\sin{X}}{\sin{Y}} \]
114 Law of Sines. SSA. $x,y$ are any two sides of any triangle and $X,Y$ are angles opposite those sides. Use this form to solve for $X$ when $x,y,Y$ are known. Use the $\mathrm{arcsin}$ function. Ambiguous case. \[ \sin{X}=\frac{x\sin{Y}}{y} \]