A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #8#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?
1 Answer
Feb 13, 2016
C ≈ 8.43
Explanation:
In this triangle , 2 sides and the angle between them are known , hence use the
#color(blue)(" cosine rule ") #
# C^2 = A^2 + B^2 - (2ABcostheta)# here A = 1 , B = 8 and
#theta = (5pi)/8 #
substitute these values into the formula
# C^2 = 1^2 + 8^2 - ( 2 xx 1 xx 8cos((5pi)/8) ) # = 1 + 64 - ( -6.12) = 65 + 6.12 = 71.12
#C^2 = 71.12 rArr C =sqrt(71.12) ≈ 8.43 #
