Question

In Δ ABC, m ∠ B=26°, a=20 in., and c=10 in. Find b .

Answer 1

`b = 10\sqrt{5-4\cos 26^(\circ)}`

Explanation:

Using the Law of Cosines,

`b^2 = a^2 + c^2 - 2ac \cos B \\ \\ b^2 = 20^2 + 10^2 - 2(20)(10)\cos 26^(\circ) \\ \\ b=\sqrt{500-400\cos 26^(\circ)} \\ \\ =10\sqrt{5-4\cos 26^(\circ)}`