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

Answer:

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 #