Law of Cosines

• Law of cosines

  Used to solve oblique triangles when given two sides and the included angle (SAS) or when given three sides (SSS)
• Steps to solve oblique triangles using law of cosines

  1. Find the side opposite the given angle (SAS)

  2. Apply law of cosines to find the unknown side

  3. Apply law of sines or cosines to find the remaining angles

  4. Use triangle sum theorem to find the third angle
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• Steps to solve SAS oblique triangle

  1. Find the side opposite the given angle

  2. Apply law of cosines to find the unknown side

  3. Apply law of sines or cosines to find the remaining angles

  4. Use triangle sum theorem to find the third angle
• Steps to solve SSS oblique triangle


  1. Find the angle opposite the longest side using law of cosines

  2. Find the remaining angles using law of sines or cosines

  3. Use triangle sum theorem to find the third angle