A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4#. If side C has a length of #4 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

1 Answer
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Jan 6, 2016

The final answer is A = B = #4*sqrt(2)#

Explanation:

We have two angles #pi/4# and #3pi/8# so by adding them and subtracting the sum from #pi# (#pi=180# = the sum of the angles of a triangle). The third angle is #pi - (3pi/8 + pi/4)# = #3pi/8#.

From the angles, we can infer that the triangle is isosceles, and we already know that #the angle between A and B = the angle between A and C#, by exclusion (since # the angle between A and B!=the angle between B and C#). Therefore, A=B.
#sin /_ between A and B =C/A= sin (pi/4) = 1/sqrt(2)#
# 4/A = 1/sqrt(2)#

#A= 4*sqrt(2)#

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