Chapter 6.2, Problem 1E

To determine

Fill in the blanks:

The standard form of the law of cosines for $CosC=\frac{a^2+b^2-c^2}{2ab}$ is__

Answer to Problem 1E

The standard form of the law of cosines for $CosC=\frac{a^2+b^2-c^2}{2ab}$ is $c^2=a^2+b^2-2ab\cos C$ .

Explanation of Solution

If the two sides and included angle of a triangle are known or if three sides are known use law of cosines which is states as below:

For a triangle with sides $a,b,c$ and opposite angles $A,B,C$ .

Then, $c^2=a^2+b^2-2ab\cos C$

  $c^2=a^2+b^2-2ab\cos C$

Rewrite the equation as,

  $\cos C=\frac{a^2+b^2-c^2}{2ab}$

Therefore, The standard form of the law of cosines for $CosC=\frac{a^2+b^2-c^2}{2ab}$ is $c^2=a^2+b^2-2ab\cos C$ .