Find the unknown parts of `DeltaABC` if `a = sqrt(3) + 1, b = sqrt(3) - 1, C=60^0`.

Explanation

In `triangleABC`,
`cos C = (a^(2)+b^(2)-c^(2))/(2abc)`
`rArr cos60^(@) = ((sqrt(3)+1)^(2) + (sqrt(3)-1)^(2) - c^(2))/(2(sqrt(3)+1)(sqrt(3)-1))`
`rArr 1/2=(3+1+2sqrt(3))+(3+1-2sqrt(3)-c^(2))/(2(3-1))`
`rArr 1/2 = (8-c^(2))/(4) rArr c=sqrt(6)`
Also, `b/(sinB) = c/(sinC) rArr (sqrt(3-1))/(sinB) = sqrt(6)/(sin60^(@)) = 2sqrt(2)`
`therefore sinB = (sqrt(3)-1)/(2sqrt(2)) rArr B=15^(@)`
Now, `angleA+angleB+angleC=180^(@)`
`rArr angleA + 15^(@) + 60^(@) = 180^(@)`
`therefore angleA=105^(@)`