Question

How do you solve the triangle given a=39, b=52, <C=122 degrees?

Answer 1

Use The Law of Cosines.

Explanation:

The Law of Cosines states that `c^2=a^2+b^2-2abcosC`. We have `a,b` and `C` and should try to find side `c`.

Plug in values.
`c^2=39^2+52^2-2(39)(52)cos122˚`
`c^2~~6374.3525`
`c~~ 79.8395`

Now, using The Law of Sines, we can figure out the other two angle lengths.

The Law of Sines states that `sinA/a=sinB/b=sinC/c`, so we can say that `sinA/39=(sin122˚)/79.8395` and `sinB/52=(sin122˚)/79.8395`.

Cross multiply and use `arcsin` to figure out angles `A` and `B`.