# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 7, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Apr 6, 2017

$C = 7$

#### Explanation:

The length of $A$ is $2$

The length of $B$ is $7$

The angle between $A$ and $B$ is $\angle c = \frac{5 \pi}{12}$

Now to the Law of Cosines

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cdot \cos c$

C=sqrt(A^2+B^2-2AB*cosc

We will simply substitute the values we have and find the length of $C$

C=sqrt(2^2+7^2-2(2)(7)*cos(5pi)/12

$\textcolor{red}{N O T E} :$ Your calculator should be in radian mode when computing this. If you cannot change it to rad then change the angle to degrees and compute it.

$\frac{5 \cancel{\pi}}{12} \times {180}^{0} / \cancel{\pi} = {75}^{0}$

C=sqrt(4+49-2(14)*cos(5pi)/12, if your calculator is in $\textcolor{red}{r a \mathrm{di} a n}$ mode

C=sqrt(4+49-2(14)*cos75^0, if your calculator is in $\textcolor{red}{\mathrm{de} g r e e}$ mode

$C = 6.76 \approx 7$