How do you find the answer to this problem without a calculator?

Question

sin (arctan 3/4)

Answer 1

tan = opp/adj

so opp = 3

adj = 4

hyp² = opp² + adj²

solving gives hyp = 5

sin = opp/hyp = 3/5

Answer 2

By knowing that the length of the hypotenuse of the right triangle that has  the perpendicular sides with lengths 3 and 4, is 5.  

Answer 3

By drawing the picture, labeling sides, using the Pythagorean relation, and knowing the defined the range of arctangency.  

sine (arctan 3/4) = 3/5 = .6.