# Find the cosine of the angle M of the triangle KLM if K (1; 7) L (-2; 4), M (2; 0).

June 30, 2021 | education

| To solve, we determine the lengths of the sides of the triangle by the coordinates of the th vertices.

KL = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2, where X1, X2, Y1, Y2 are the coordinates of points.

KL = √ (-2 – 1) ^ 2 + (4 – 7) ^ 2 = √ (9 + 9) = √18 = 3 * √2 cm.

KM = √ (2 – 1) ^ 2 + (0 – 7) ^ 2 = √ (1 + 49) = √50 = 5 * √2 cm.

ML = √ (2 – (-2) ^ 2 + (0 – 4) ^ 2) = √ (16 + 16) = √32 = 4 * √2 cm.

Let’s define the type of triangle by the Pythagorean theorem.

The large side of the triangle is 5 * √2 cm.

(5 * √2) ^ 2 = 50.

(3 * √2) ^ 2 + (4 * √2) ^ 2 = 18 + 32 = 50.

50 = 50, triangle KLM right-angled with hypotenuse KM and right angle L.

Then the cosine of the angle KML will be: CosKML = ML / MK = (4 * √2) / (5 * √2) = 4/5 = 0.8.

Answer: CosKML = 0.8.

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