Town B is 45 Km Due North of town A. Town C is 38 Km from Town A in a Direction of 062 Degrees. Calculate The Distance of Town B from Town C

So we have triangle ABC with AB = 45, AC = 38, and an included angle BAC = (90 - 62) = 28°

And we're looking for BC. We can use the Law of Cosines for this.

BC² = AB² + AC² - 2(AB)(AC)cos28°

BC² = (45)² + (38)² - 2(45)(38)cos28°

BC² = 449.31923242222   ...and taking the square root, we have

BC ≈ 21.2 km