Question

Using the cosine law to determine the measure of we could use _______:

Answer 1

- The Cosine law is given below as:

`\begin{gathered} Given\text{ }\triangle ABC,\text{ with sides }a,b,c\text{ and angles }\angle A,\angle B,\angle C\text{ such that} \\ a\text{ is opposite }\angle A \\ b\text{ is opposite }\angle B \\ c\text{ is opposite }\angle C \\ \\ \text{ We have:} \\ a^2=b^2+c^2-2(bc)\cos\angle A \end{gathered}`

- We can make
`\begin{gathered} a^2=b^2+c^2-2bc\cos\angle A \\ \text{ Subtract }b^2\text{ and }c^2\text{ from both sides} \\ \\ a^2-b^2-c^2=-2bc\cos\angle A \\ \\ \text{ Divide both sides by }-2bc \\ \cos\angle A=(a^2-b^2-c^2)/(-2bc) \\ \text{ } \\ \text{ Take the cos inverse of both sides} \\ \\ \therefore\angle A=\cos^(-1)((a^2-b^2-c^2)/(-2bc)) \end{gathered}`

Final Answer

The answer is