Question

The cosine rule calculate tha angle of r 7.2 3,7 5.2

Answer 1

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,

$a^2=b^2+c^2-2bc\cos A$

Using the Law of Cosine, we get

$(7.2)^2=(3.7)^2+(5.2)^2-2(3.7)(5.2)\cos r$

$51.84=13.69+27.04-38.48\cos r$

$51.84=40.73-38.48\cos r$

$51.84-40.73=-38.48\cos r$

On further simplification, we get

$11.11=-38.48\cos r$

$\dfrac{11.11}{-38.48}=\cos r$

$-0.2887=\cos r$

$\cos^{-1}(-0.2887)=r$

$106.780143=r$

$r\approx 106.78$

Therefore, the measure of angle r is 106.78 degrees.