A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #5#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?
1 Answer
Feb 5, 2016
C ≈ 3.66
Explanation:
Given a triangle with 2 sides and the angle between them known ,use the
#color(blue)(" cosine rule ")color(black)(" to solve for C")# In relation to this triangle the cosine rule is :
# C^2 = A^2 + B^2 - ( 2ABcostheta) # where
#theta color(black)(" is the angle between A and B")# here A = 7 , B = 5 and
#theta = pi/6 #
#rArr C^2 = 7^2 + 5^2 - [ 2 xx 7 xx 5 xx cos(pi/6)] # = 49 + 25 - ( 60.6217..) ≈ 13,38
( remember this is
#C^2 # )
#rArr C = sqrt13.38 ≈ 3.66#
