# How do you find the exact value of the third side given triangle ABC, a=62.5, b=44.7, mangleC=133?

Apr 17, 2017

Third side $c = 98.565$

#### Explanation:

We can use the cosine formula to find the length of a side or size of an angle. For a triangle with sides $a , b$ and $c$ and angles $A , B$ and $C$ the cosine rule can be written as ${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos A$.

Here $a = 62.5$, $b = 44.7$ and m/_C=133°, hence

c^2=62.5^2+44.7^2-2×62.5×44.7×cos133°

= 3906.25+1998.09-125×44.7×(-0.682)

= $3906.25 + 1998.09 + 3810.675$

= $9715.015$

Hence $c = \sqrt{9715.015} = 98.565$