Find the cosine of angle A in triangle ABC, where A (0.2), B (3.0), C (4.1).

univerkov | January 10, 2021 | education

Knowing the coordinates of the vertices of the triangle, we determine the lengths of its sides.
AB = √ (X2 – X1) ^ 2 + (Y2 – Y2) ^ 2 = √ (3 – 0) ^ 2 + (0 – 2) ^ 2 = √13 cm.
ВС = √ (4 – 3) ^ 2 + (1 – 0) ^ 2 = √2 cm.
AC = √ (4 – 0) ^ 2 + (1 – 2) ^ 2 = √17 cm.
Let us apply the cosine theorem.
BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * AC * CosA.
2 = 13 + 17 – 2 * √221 * CosA.
2 * √221 * CosA = 28.
CosA = 28/2 * √221 = 0.94.
Answer: The cosine of angle A is 0.94.

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