Given:
[tex]a=154\text{ }km,\text{ }b=230\text{ }km,\text{ }c=199\text{ }km,\text{ and }\angle B=\theta.[/tex]
Required:
We need to find the measure of the angle.
Explanation:
Consider the cosine law.
[tex]b^2=a^2+c^2-2ac\text{ }cosB[/tex][tex]-\frac{b^2-a^2-c^2}{2ac}=cosB[/tex][tex]cosB=\frac{a^2+c^2-b^2}{2ac}[/tex][tex]Substitute\text{ }a=154\text{ }km,\text{ }b=230\text{ }km,\text{ }c=199\text{ }km,\text{ and }\angle B=\theta\text{ in the equation.}[/tex][tex]cos\theta=0.6039[/tex][tex]\theta=52.8493\degree[/tex][tex]\theta=52.8\degree[/tex]
Final answer:
[tex]\theta=52.8\degree[/tex]
