# How do you find the length of side c for the triangle with dimensions A = 57° , a = 11, b = 10?

Sep 12, 2015

Find Angle B, then, with A and B we can find angle C. Knowing C will allow us to find c.

#### Explanation:

$\sin B = \frac{10}{11} \sin {57}^{\circ}$

So $B \approx {49.7}^{\circ}$

$C = {180}^{\circ} - A - B \approx {73.3}^{\circ}$

$c = \frac{11}{\sin {57}^{\circ}} \sin {73.3}^{\circ} \approx 12.6$

It is $c = 10 , 059$

#### Explanation:

We can use the law of cosines hence

c^2=a^2+b^2-2abcosA=>c^2=(11)^2+(10)^2-2*10*11*cos(57)=> c=10,059