In the triangle ABC AC = BC, angle C is 120 degrees, AB = √3, find AC.
| September 2, 2021 | education
Using the cosine theorem, we get:
AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AB * BC * cos (C).
Substituting the known values, we get:
AB ^ 2 = 2 (√3) ^ 2 – 2 * (√3) ^ 2 * cos (120 °) = 6 * (1 – cos (120 °)) = 6 * (1 – (-1/2) = 9.
Then:
AB = √9 = 3.
Answer: the desired side AB is 3.
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