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
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)