To find sin(2a), we can use the double angle identity for sine:

sin(2a) = 2sin(a)cos(a)

Given that tan(a) = 3/4, we know that we can form a right triangle with opposite side length 3 and adjacent side length 4. Using the Pythagorean theorem, we can find the hypotenuse:

(3)^2 + (4)^2 = c^2
9 + 16 = c^2
25 = c^2
c = 5

Now, we can find sin(a) and cos(a):

sin(a) = opposite/hypotenuse
sin(a) = 3/5

cos(a) = adjacent/hypotenuse
cos(a) = 4/5

Now, we can find sin(2a):

sin(2a) = 2sin(a)cos(a)
sin(2a) = 2(3/5)(4/5)
sin(2a) = 24/25

Therefore, sin(2a) = 24/25.