In triangle ABC AC = BC AB = 3 sin A = √3 / 2, find AC
| June 15, 2021 | education
Since AC = BC, the triangle is isosceles and the angles ABC and BAC are equal.
Since sin (BAC) = √ (3) / 2, then BAC = 60 degrees.
ABC is then also 60 degrees.
Since the sum of the angles of the triangle is 180 degrees, then
ABC + BAC + ACB = 180
ACB = 180 – 60 – 60 = 60
This means that the triangle is equilateral and AC = AB = 3 cm.
Answer: 3 cm.
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