Question

How do you use the law of cosines or law of sines if you are given a = 4, b = 3 and c = 6?

Answer 1

You can use the Law of Cosines to calculate the angles of the triangle.

`A~~36.3` degrees
`B~~117.3` degrees
`C~~26.4` degrees

Explanation:

In this case the only thing you need to solve this triangle is to calculate the angles.

To calculate angle `A` you use:

`a^2=b^2+c^2-2*b*c*cosA`
so you calculate:

`4^2=3^2+6^2-2*3*6*cosA`
`16=9+36-36cosA`
`36cosA=9+36-16`
`36cosA=29`
`cosA=29/36`
`A~~36.3` degrees

The same way you can calculate C

`c^2=a^2+b^2-2*a*b`
`6^2=3^2+4^2-2*3*4*cosC`
`36=9+16-24cosC`
`36-9-16=-24cosC`
`11=-24cosC`
`cosC=-11/24`
`C~~117.3` degrees.

Now you can calculate B either using the Law of Cosines again or using the fact, that the sum of angles in triangle equals to 180 degrees.

`A+B+C=180`
`36.3+B+117.3=180`
`B=180-117.3-36.3`
`B~~26.4`