Question

PLEASE HELP MY ASSIGNMENT IS OVERDUE

In the triangle ABC, AB = (x + 3)cm, BC = (x + 2)cm, AC = x cm and angle BAC = 60degrees

Find the value of x.

Answer 1

x would equal 5 in the problem

Answer 2

• x = 5

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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