∵π/6＜α＜π/2
∴0＜α-π/6＜π/3
∴sin（α-π/6）=5/13
∴sinα=sin[(α-π/6)+π/6]
=sin(α-π/6)cosπ/6+cos(α-π/6)sinπ/6
=5/13*(√3/2)+12/13*(1/2)
=(5√3+12)/26
【过程已写出,】