Question

Three circles with radii 35cm, 50cm, and 65cm respectively are tangent to each other externally. Find the angles of the triangle formed by joining the centers of the circles.

My teacher said to use the cosine law cause you know 3 sides but no angles. But I can't figure it out.
The answer is suppose to be angle A=57.69 degrees.....so on...
But I still can't figure out how to do it

Answer 1

If you draw the triangle and label the sides a,b,c and the angles A, B, C, then
c^2 = a^2+b^2-2*a*b*cos C
I labeled them arbitrarily and worked the cos law three times and came up with angles of 76.4, 57.7 and 45.9 and all of that adds up to 180 degrees.

Answer 2

G