Question

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8. In Traingle ABC, BC = 4 cm, M is the mid-point of
BC, AM = 4 cm and AMB = 120°. Calculate
(a) AC;
(b) AB;
(c) angle ACB.​

Answer 1

Answer:

Step-by-step explanation:

<AMC = 180º − <AMB

 <AMC = 180º − 120º

 <AMC = 60º

 Now use the law of cosines twice to find AC and AB:

1.

   (AC)² = (AM)² + (MC)² − { 2 • (AM) • (MC) • cos[AMC] }

   (AC)² = 4² + 2² − { 2 • 4 • 2 • cos[60] }

   AC = 3.46 cm

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2.

   (AB)² = (AM)² + (MB)² − { 2 • (AM) • (MB) • cos[AMB] }

   (AB)² = 4² + 2² − { 2 • 4 • 2 • cos[120] }

   AB = 5.29 cm

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3.

   (AM)² = (CM)² + (AC)² − { 2 • (CM) • (AC) • cos[ACB] }

            4² = 2² + (3.46)² − { 2 • (2) • (3.46) • cos[ACB] }

   cos[ACB] = 0

      <ACB = 90º

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