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`

`(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.