We know that

**sin (x + y) = sin x cos y + cos x sin y** ... (1)

Now cos^{2}x = 1 – sin^{2}x = 1 – 9/25 = 16/25

Therefore **cos x = ± 4/5.**

Since x lies in** second quadrant, cos x is negative. **

Hence **cos x = −4/5 **

Now sin^{2}y = 1 – cos^{2}y = 1 – 144/169 = 25/169

i.e.** sin y = ± 5/13. **

Since y lies in **second quadrant, hence sin y is positive**.

Therefore,** sin y =5/13.**

Substituting the values of sin x, sin y, cos x and cos y in (1), we get

sin(x + y) 3/5 × (-12/13) + (−4/5) × 5/13 = (-36/65) –(20/65) = -56/65

Therefore, **sin(x+y) = ****-56/65**