A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #7#, respectively, and the angle between A and B is #(3pi)/4 #. What is the length of side C?

1 Answer
Feb 9, 2016

Answer:

# C = sqrt(74 + 35 sqrt(2)) ~~ 11.11 #

Explanation:

Let the angle between #A# and #B# be #gamma = (3pi)/4#.

Then, the length of side #C# can be computed with the law of cosines:

#C^2 = A^2 + B^2 - 2AB*cos(gamma)#

# = 5^2 + 7^2 - 2*5*7*cos((3pi)/4)#

# = 74 - 70 cos((3pi)/4)#

# = 74 - 70 * ( - cos(pi/4))#

# = 74 + 70 * sqrt(2)/2#

# = 74 + 35 sqrt(2)#

Thus,

# C = sqrt(74 + 35 sqrt(2)) ~~ 11.11 #