Given:
Consider the below figure attached with this question.
To find:
The measure of angle r by using the cosine rule.
Solution:
According to Law of Cosine,
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Using the Law of Cosine, we get
[tex](7.2)^2=(3.7)^2+(5.2)^2-2(3.7)(5.2)\cos r[/tex]
[tex]51.84=13.69+27.04-38.48\cos r[/tex]
[tex]51.84=40.73-38.48\cos r[/tex]
[tex]51.84-40.73=-38.48\cos r[/tex]
On further simplification, we get
[tex]11.11=-38.48\cos r[/tex]
[tex]\dfrac{11.11}{-38.48}=\cos r[/tex]
[tex]-0.2887=\cos r[/tex]
[tex]\cos^{-1}(-0.2887)=r[/tex]
[tex]106.780143=r[/tex]
[tex]r\approx 106.78[/tex]
Therefore, the measure of angle r is 106.78 degrees.
