A triangle has side cequals=1010 and angles aequals=startfraction pi over 4 endfraction π 4 and bequals=startfraction pi over 3 endfraction π 3. find the length a of the side opposite

a.

Angle C is π - (π/4) - (π/3) = 5π/12. The Law of Sines tells you

... a/sin (A) = c/sin (C)

... a = sin (A) ·c/sin (C)

... a = sin (π/4) ·10/sin (5π/12) ≈ 7.32

The length of the side opposite angle A is about 7.32.