Question

In Δ ABC, a=8m, b=5 m , and c=10 m . Find m∠ A .

Answer 1

arccos(51/100)

Explanation:

By the Law of Cosines,

`a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=(b^2 + c^2 - a^2)/(2bc) \\ \\ m\angle A=\arccos \left((b^2 + c^2 - a^2)/(2bc) \right) \\ \\ =\arccos \left((10^2 + 5^2 - 8^2)/(2(5)(10)) \right) \\ \\ =\arccos(51/100)`