If in the triangle ABC the sides AB = 8, BC = 15, AC = 17 are given, then what is the sine of A.

univerkov | May 17, 2021 | education

Since we know the lengths of all sides of the triangle, we apply the cosine theorem for a triangle to solve.

BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * AC * CosA.

15 ^ 2 = 8 ^ 2 + 17 ^ 2 – 2 * 8 * 17 * CosA.

226 = 64 + 289 – 272 * CosA.

272 * CosA = 128.

CosA = 128/272 = 8/17.

Then Sin2A = 1 – Cos2A = 1 – 64/289 = 225/289.

SinA = 15/17.

Answer: SinA = 15/17.

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