Question

How do you solve `13^2=8^2+6^2-2(8)(6)cosA`?

Answer 1

`angleA=136^@`

Explanation:

`"isolate "cosA" by evaluating the numeric values"`

`rArr169=64+36-96cosA`

`rArr-96cosA=69`

`rArrcosA=-69/96=-23/32`

`rArrA=cos^-1(-23/32)=136^@`

Answer 2

`rArrA = 136^o +2kpi" "` where `k in NN`
`" "`
Or
`rArr A=224^o +2kpi" "`where `k in NN`

Explanation:

`13^2-8^2-6^2=-2 (8)(6)cosA`
`" "`
`rArr169-64-36 =-2 (8)(6)cosA`
`" "`
`rArr169-64-36 = -96cosA`
`" "`
`rArr 69 = -96cosA`
`" "`
`rArrcosA = -69/96`
`" "`
`rArr CosA = -0.71875`
`" "`
Since `cosA <0" "`then `A^o in` quadrants 2&3
`" "`
`rArrA = 136^o +2kpi" "` where `k in NN`
`" "`
Or
`rArr A=224^o +2kpi" "`where `k in NN`