9-4 Law of Cosines

This week I am going to teach you how to use law of cosines. You use it to solve non-right triangles. It is only used when Pythagorean and law of sines do not work. It is pretty easy. (Capital letters represent angles, and lowercase letters represent legs).
There is only one formula that you need to remember for this section:
(opposite leg^2) = (adjacent leg^2) + (other adjacent leg^2) – 2 (adjacent leg) (other adjacent leg) cos (angle between)
Example 1:
In triangle ABC, C= 60 degrees, b= 5, and a= 8. Solve the triangle.
• First, you have to draw a picture of the triangle described. (Make sure the letters are in alphabetical order going clockwise.
• Next, you would find leg c because it is opposite of the given angle, C.
• Plug into the formula: c^2= (5^2) + (8^2) – 2 (5) (8) cos (60 degrees)
• Take the square root of both sides (plug into calculator exactly as is): c= 7
• Now you would find angle A by plugging into the formula: 8^2= (5^2) + (7^2) – 2 (5) (7) cos A
• Cos A= ((8^2) - (5^2) – (7^2)) / ((-2 (5) (7)
• Take the inverse and plug it into your calculator: A= 81.787 degrees
• Add the two angles and subtract them from 180: B= 32.213 degrees