A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #4#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

1 Answer
Jun 25, 2017

Answer:

#~~8.026#

Explanation:

#"to calculate c use 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)|)))#

#"here " a=6,b=4" and "C=(7pi)/12#

#c^2=6^2+4^2-(2xx6xx4xxcos((7pi)/12))#

#color(white)(c^2)=36+16-48cos((7pi)/12)#

#color(white)(c^2)~~64.4233#

#rArrc=sqrt(64.4233)~~8.026" to 3 dec. places"#