+128460 We have a SSA situation.....I'm assuming the greater possible value for BC
Use Law of Cosines to find BC
9^2 = 10^2 + BC^2 -2 (10) (BC)cos 60
81 - 100 = BC^2 - 10BC
-19 = BC^2 - 10BC
BC^2 - 10BC + 19 = 0
BC^2 -10BC = -19 complete the square on BC
BC^2 - 10BC + 25 = -19 + 25
(BC - 5)^2 = 6 take the positive root
BC - 5 = sqrt 6
BC = 5 + sqrt 6
Area = (1/2)(AC)(BC) sin 60 = (1/2) (5 +sqrt 6) (10) (sin 60) = 5 (5 + sqrt 6) ( sqrt (3) / 2 ) ≈
32.26 units^2
