Find the cosine of the angle a of the triangle ABC if A (3: 9) B (0: 6) C (4: 2).
| February 22, 2021 | education
Let’s define the coordinates of the vector AB and AC.
AB = (X2 – X1); (U2 – U1) = (-3; -3).
AC = (X2 – X1); (U2 – U1) = (1; -7).
Knowing the coordinates of the vectors AB and AC, we determine the cosine of the angle between them.
CosA = (X1 * X2) + (Y1 * Y2) / √ (X1 ^ 2 + X2 ^ 2) * √ (Y1 ^ 2 + Y2 ^ 2) = (-3 + 21) / √18 * √50 = 18 / √900 = 18/30 = 3/5 = 0.6.
Answer: The cosine of the angle is 0.6.
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