Answer:
a = 22
Step-by-step explanation:
The law of cosines can be written 3 different ways for a triangle, each way with a different angle. Here, the given angle is angle A, so we write the law of cosines with angle A.
[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]
[tex] a^2 = 15^2 + 12^2 - 2(15)(12) \cos 110^\circ [/tex]
[tex] a^2 = 225 + 144 - 360 \cos 110^\circ [/tex]
[tex] a^2 = 369 - 360(-0.34202) [/tex]
[tex] a^2 = 369 + 123.12725 [/tex]
[tex] a^2 = 492.12725 [/tex]
[tex] a = \sqrt{492.12725} [/tex]
[tex] a = 22 [/tex]
