PLEASE HELP MY ASSIGNMENT IS OVERDUE In the triangle ABC, AB = (x + 3)cm, BC = (x + 2)cm, AC = x cm and angle BAC = 60

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.

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bonexptip 4 weeks 2022-12-21T11:27:35+00:00 2 Answers 0 views 0

Answers ( 2 )

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    2022-12-21T11:28:44+00:00

    x would equal 5 in the problem

  1. Answer:
    • x = 5
    ———————————
    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

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