Find the exact value of the trigonometric function given tha

Find the exact value of the trigonometric function given that

sin u = 7/25

and

cos v = 3/5

(Both u and v are in Quadrant III.)

sin(u + v)

sin u=-7/25

here opposite=7 and hypotenuse=-25

Therefore adjacent= sqrt(7^2-(-25)^2)= sqrt(576)=24

Therefore cos u= -24/25

cos v= -3/5

Here adjacent=3 and hypotenuse=-5

THerefore opposite=sqrt((-5)^2-3^2= sqrt16)=4

Therefore sin v=-4/5

sin(u+v)=sinu cosv + cosu sinv

= (-7/25)(-3/5)+(-24/25)(-4/5)= (21/625)+(96/125)= 117/125