# In Triangle ABC, if a=3, b=5, and cosC=1/5, how do you find the exact value of c?

Oct 17, 2017

$c = 2 \sqrt{7}$

#### Explanation:

we use the cosine rule

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

we have all the information required

so

c^2=3^2+5^2-(2xx3xxcancel(5)xx1/cancel5))

${c}^{2} = 9 + 25 - 6$

${c}^{2} = 28$

$c = 2 \sqrt{7}$