Find the cosines of the angles A, B, C if A (3: 9), B (0.6), C (4.2).

Let’s look at how to find the cosine of the angle A, and the rest can be solved similarly.

So, we start by applying the formula for the coordinates of a vector through the coordinates of its end and beginning, and to calculate the cosine of an angle, we will use the formula for their coordinates.

To find the cosine of the angle A, we need to know the lengths of the vectors by vectors AB and AC.

cos A = (x1 * x2 + y1 * y2) / (√ (x1 ^ 2 + x2 ^ 2) * √ (y1 ^ 2 + y2 ^ 2)).

Vector AB has coordinates (-3; -3), AC (1; -7).

cos A = (-3 + 21) / √18 * √50 = 6 / (2 * 5) = 3/5 = 0.6.