If a triangle has three sides with length of 9,7,6. What is measure of the internal angle α between the sides of 9, 6?

#### Question

#### Answer

Given the length of three sides of a triangle, the internal angles could be determined by using the Law of Cosines

\cos A = \dfrac{b^2+c^2-a^2}{2bc}

Substitute the given values into the formula ,

\cos A=\dfrac{9^2+6^2-7^2}{2\times 9\times 6 }

=\dfrac{81+36-49}{2\times 9\times 6 }

=\dfrac{94}{2\times 9\times 6 }

=\dfrac{47}{54}

Therefore, the angle between the sides of 9 and 6 is \arccos\dfrac{47}{54}