The three circles are arranged so that they touch each other

The three circles are arranged so that they touch each other, as shown in the figure. Use the given radii for the circles with centers A, B, and C, respectively, to solve triangle. 5.3, 4.2, 3.2 A = degree (Do not round until the final answer. Then round to the nearest degree as needed.) B = degree (Do not round until the final answer. Then round to the nearest degree as needed.) C = degree (Do not round until the final answer Then round to the nearest degree as needed.)

Solution

distance AC = 5.3 + 3.2 = 8.5

distance AB = 5.3 + 4.2 = 9.5

distance BC = 4.2 + 3.2 = 7.4

therefore applying law of cosines

a^2 = b^2 + c^2 - 2bc cos A

angle A = 48 degrees

again applying law of cosines to find angle B

angle B = 59 degrees

angle C = 180 - ( 59 + 48 )

C = 73 degrees