A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #2#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?
1 Answer
Feb 10, 2016
≈ 3.24
Explanation:
In this triangle , 2 sides and the angle between them are known , hence use the 'cosine rule '.
for this triangle the cosine rule is :
# C^2 = A^2 + B^2 - (2ABcos(pi/8) )#
# C^2 = 5^2 + 2^2 - (2 xx 5 xx 2 xxcos(pi/8))#
#= 25 + 4- ( 20cos(pi/8)) = 29- (18.478 ) = 10.522#
# C^2 = 10.522 rArr C =sqrt10.522 ≈ 3.24 #
