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

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Answer 1 · 2017-01-16T23:23:04

#C = 5sqrt(2-sqrt2)#

Using the law of cosines, that states that if #A,B,C# the lengths of the sides of a triangle, then

#C^2 = A^2 + B^2 - 2ABcosθ#

where #θ# is the angle between #A# and #B#.

#C^2 = 25 + 25 - 50cos(π/4)#

#cos(π/4) = sqrt2/2#

#C^2 = 50 - 25sqrt2#

#C = sqrt(50 - 25sqrt2) = sqrt(25(2-sqrt2)) = 5sqrt(2-sqrt2)#