A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #8#, respectively, and the angle between A and B is #pi/4#. What is the length of side C?

1 Answer
Dec 22, 2015

Answer:

#c=5.67# rounded to hundredth.

Explanation:

Cosine Law

#c^2 = a^2 + b^2 - 2abcos(theta)#

In our problem #a = 6# and #b=8# and we are also given the angle between as #pi/4#

To find #c# we plug in the values in the cosine law and we get.

#c^2 = 6^2 + 8^2 - 2*6*8*cos(pi/4)#
#c^2 = 36 + 64 - 96 (sqrt(2)/2)#
#c^2 = 100 - 48*sqrt(2)#
#c^2 = 32.117749006091437657518941237934# using calculator
#c = sqrt(32.117749006091437657518941237934)#
#c = 5.6672523330174242081448041317437#

#c=5.67# rounded to hundredth.