Question

Question #554be

Answer 1

`C~~11.65`
Angle `A` will be `49.5` degrees.
Angle `B` will be `30.5` degrees.

Explanation:

To find `C`, arrange the cosine rule in terms of `C`:

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

You have `a=9`, `b=6`, `C=100`, therefore

`c^2=81+36-108cos100`
`c^2=117-(-18.7540031873)=135.754003187`
`c=sqrt(135.754003187)=11.6513519897~~11.65`

To find angle `A`, arrange the rule like this

`A=cos^-1((b^2+c^2-a^2)/(2bc))`

Plug in values for `a`, `b`, and `c` (that you have just found),

you get

`A=cos^-1((36+135.754003187-81)/(139.82))=cos^-1((90.75)/(139.82))`

`A~~49.5` degrees

In a triangle, the total sum of the degrees is always `180`.

We have found two angles `A` and `C`.

So, `B=180-49.5-100=30.5` degrees.