A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #1#, respectively, and the angle between A and B is #(7pi)/8 #. What is the length of side C?

1 Answer
Feb 8, 2016

Answer:

#C ~~ 6.93#

Explanation:

You can use the law of cosines here.

Let the angle opposite to side #A# be #alpha#, the angle opposite to side #B# be #beta# and the angle opposite to side #C# be #gamma#.

Then the law of cosines states:

#C^2 = A^2 + B^2 - 2ABcos(gamma)#

# = 6^2 + 1^2 - 2*6*1cos((7pi)/8)#

# = 37 - 12cos((7pi)/8)#

# ~~ 37 - 12 * (-0.92)#

# ~~ 48.09 " units"^2#

Thus,

#C ~~ 6.93 " units"#