If theta is an acute angle such that sin theta=5/13, what is the value of sin2 theta

cosӨ= 12/13

sin 2Ө= 2 sinӨcosӨ = 2 (5/13)(12/13) = 120/169

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

now since a is acute and cos(a) = sqrt(1 - (5/13)^2)

=> cos(a) = 12/13

=> sin(2a) = 2sin(a)cos(a) = 2 * (5/13) * (12/13) = 120/169

sin2theta = 2 sin theta cos theta

then you have to fin the value of cos theta

which is root 1-25/13^2 unit circle

12/13

then sin 2 theta = 2 * 5/13 * 12/13
= 12/169