Answer:
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Side BC is opposite to ∠BAC and adjacent sides are AB and AC.
Use the law of cosines:
- BC² = AB² + AC² - 2AB*AC*cos ∠BAC
Substitute and solve for x:
- (x + 2)² = (x + 3)² + x² - 2x(x + 3) cos 60°
- x² + 4x + 4 = x² + 6x + 9 + x² - 2(x² + 3x)*1/2
- x² + 4x + 4 = 2x² + 6x + 9 - x² - 3x
- x² + 4x + 4 = x² + 3x + 9
- 4x - 3x = 9 - 4
- x = 5
