A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #2#, respectively, and the angle between A and B is #(2pi)/3 #. What is the length of side C?
1 Answer
Mar 25, 2016
≈ 7.211 units
Explanation:
Given a triangle , where 2 sides and the angle between them are known, we can use the
#color(blue)" cosine rule " " to find C "#
# c^2 = a^2 + b^2 - (2ab costheta) # where a and b are the 2 known sides and
#theta" the angle between them " # here a = 6 , b = 2 and
# theta = (2pi)/3 # substitute these values into the equation
#rArr c^2 = 6^2 + 2^2 - [2xx6xx2xxcos((2pi)/3) ] # = 36 + 4 - (-12) = 52
now
# c^2 = 52 rArr c = sqrt52 ≈ 7.211#
