A triangle has sides A, B, and C. Sides A and B are of lengths #9# and #5#, respectively, and the angle between A and B is #(5pi)/12 #. What is the length of side C?
1 Answer
Feb 10, 2016
≈ 9.1
Explanation:
In this triangle , 2 sides and the angle between them are known , so use the ' cosine rule"
For this triangle the cosine rule is ;
# C^2 = A^2 + B^2 - (2ABcos((5pi)/12) )#
# = 9^2 + 5^2 - (2 xx 9 xx 5 xx 0.2588 )# = 81 + 25 - 23.3 = 106 - 23.3 = 82.7
now
# C^2 = 82.7 rArr C = sqrt82.7 ≈ 9.1#
