Use the Law of Cosines to find the missing angle.
Find m∠B, given a = 11, b = 12, and c = 17.
+9466 According to the Law of Cosines,
b2 = a2 + c2 - 2ab cos B
Plug in the given values for a , b , and c .
122 = 112 + 172 - 2(11)(17) cos B
Simplify each side of the equation.
144 = 121 + 289 - 374 cos B
144 = 410 - 374 cos B
Subtract 410 from both sides of the equation.
144 - 410 = -374 cos B
-266 = -374 cos B
Divide both sides ny -374 .
-266 / -374 = cos B
133 / 187 = cos B
Take the inverse cosine of both sides.
B = arccos(133/187)
Plug in arccos(133/187) into a calculator to get that...
B ≈ 44.665°
