Question

How do you use the law of cosines or law of sines if you are given a = 4, b = 5, and c = 6?

Answer 1

You can use the Law of Cosines to find the remaining angles.

Explanation:

If you mark angles as:
`A` the angle opposite to side `a`
`B` the angle opposite to side `b`
`C` the angle opposite to side `c`

Then from the Law of Cosines you have:

`c^2=a^2+b^2-2abcosC`

After substituting you get:

`6^2=5^2+4^2-2*5*4*cosC`

`36=25+16-40cosC`

`40cosC=41-36`

`cosC=1/8`

`C~~82.8 deg`

If you repeat simmilar calculations for `B` you get:

`cosB=9/16`

`B~~55.77 deg`

Now you can calculate the remaining angle either using the Law of Cosies again or using the property of Sum of Angles in a Triangle

`A+B+C=180`
`A=180-B-C`
`A=180-55.77-82.8`
`A~~41.43deg`