Question

find the Sine of angle T

there are two similar right triangles, one has unknown lengths and angles which are classified as R, P, T, the other triangle has Line RQ which has a length of 60, Line QS which has a length of 25, and Line RS which has a length of 65

Angle T corresponds with angle S

Answer 1

In triangle RQS, RS = 65 is the hypotenuse and the side opposite angle S is RQ = 60, so sin S = 60/65 = 12/13.
Since angle T corresponds to angle S in the similar triangles, sin T = 12/13 (≈ 0.9231).