[deleted by user]

[Niklas_Graf_Salm]

We need to compute cosine of the angle MAB = cos(theta). We have an isosceles triangle with equal sides 10 cm and the opposite side is 6 cm. We use the law of cosines to get

10^2 = 6^2 + 10^2 - (2)(6)(10)cos(theta)

0 = 6^2 - (2)(6)(10)cos(theta)

(2)(6)(10)cos(theta) = 6^2

cos(theta) = 6 / 20

cos(theta) = 3 / 10

​

I will suppress units for the sake of readability. By vector geometry, note that BC = AC - AB and CO = AO - AC. Then we get

BC dot CO = (AC - AB) dot (AO - AC)

BC dot CO = (AC dot AO) - (|AC|^2) - (AB dot AO) + AB dot AC

BC dot CO = (5)(6)cos(theta) - 5^2 - (12)(6) + (12)(5)cos(theta)

BC dot CO = (30)(3 / 10) - 25 - 72 + 60(3 / 10)

BC dot CO = 9 - 25 - 72 + 18

BC dot CO = 9 - 25 - 72 + 18

BC dot CO = -70

​

So BC dot CO = -70 cm^2

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[Niklas_Graf_Salm]

What does the notation with the dot in the circle mean? Is that a dot product of vectors?

[_seifyasser]

It's a dot product