Chapter 1, Problem 16P

The three shown circles, with radius 15 in.,

10.5 in., and 4.5 in., are tangent to each other.

(a) Calculate the angle ? (in degrees) by using the law of cosines.

(Law of cosines: $c^2{a}^2+b^2-2abcos\gamma$)

(b) Calculate the angles $\gamma$ and $\alpha$ (in degrees) using the law of sines.

(c)Check that the sum of the angles is 180°.