Question

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.

Answer 1

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.