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

##### 1 Answer

Aug 25, 2017

#### Answer:

#### Explanation:

#"calculate C using the "color(blue)"cosine rule"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(c^2=a^2+b^2-2abcosC)color(white)(2/2)|)))#

#"where "angle C" is the angle between a and b"#

#"here "a=7,b=5" and "angle C=(5pi)/12#

#c^2=7^2+5^2-(2xx7xx5xxcos((5pi)/12))#

#color(white)(c^2)=49+25-18.117...#

#rArrc=sqrt(74-18.117...)~~ 7.5" to 1 dec. place"#