College Algebra & Trigonometry, 2018a

11.3. THE LAW OF COSINES 493
In example 3, we’ll look at a problem in which three side lengths are given and
we find an angle using the Law of Cosines.
Example 3
Solve the triangle: a =20, c =9, b =15
Round angle measures to the nearest 10 th .
A
b =15
c =9
C
a =20
B
It doesn’t matter which angle we choose to solve, but whichever angle we choose
must correspond to the side isolated on the left-hand side of the formula. If we
want to solve for ∠B, we would say:
b 2 = a 2 + c 2 − 2ac cos B
15 2 =20 2 +9 2 − 2 ∗ 20 ∗ 9 ∗ cos B
225 = 400 + 81 − 360 ∗ cos B
225 = 481 − 360 cos B
−256 = −360 cos B
−256 cos B
−360
=−360
−360
0.71 =cosB