Question

find the sine of angle R

there are two similar right triangles, one has unknown lengths and angles which are classified as T, R, S, the other triangle has Line WV which has a length of 4, Line WU which has a length of 5, and Line UV which has a length of 3

Answer 1

I need to know which vertices correspond, but a common convention is that triangle TRS corresponds in order to triangle WUV (T↔W, R↔U, S↔V). Under that correspondence:

- In triangle WUV the hypotenuse WU = 5 and the side opposite U is WV = 4, so sin(U) = 4/5.
- Therefore sin(R) = sin(U) = 4/5.

If the correspondence is different, tell me which vertex of the 3-4-5 triangle matches R and I’ll give the correct value (the other possibilities are 3/5 or 1).