Chapter 7

Chapter 7

1. 7.1

   • Law of Sines
     • (sine of alpha)/a = (sine of Beta)/b = (sine of gamma)/c
       • alpha, beta, and gamma are all the angles going right to left.
       • abc are all the sides going left to right, with b being the biggest.
       • do with non-right triangles since Pythagorean's theorem doesn't work
         • Area of a non right triangle = 1/2*side*side2*sine theta
     • Situations this applies to
       • Angle, Angle, Side
         • Angle, Side, Angle
           • Side, Side, Angle
             • Side, Angle, Side
     • largest angle is opposite the longest side since the two angles adding up to its supplementary angle are smaller than it

2. 7.2

   • Just practical applications of Law of Sine

3. 7.3

   • Law of Cosine
     • x^2 = y^2 +z^2 - 2yz*cos(theta)
       • c^2 = a^2+b^2-2ab*cosine(gamma)
       • a^2 = b^2+c^2-2bc*cosine(alpha)
       • b^2 = a^2+c^2 - 2ac*cos(beta)
     • applies to
       • side side side
         • side, angle, side
           • Side side angle
   • heron's formula: square root of (half of the perimeter)*(half of the perimeter - a)*(half of the perimeter-b)*(half of the perimeter-c)