For this problem, I found the height of the triangle first, which is \(\sqrt{8^2-5^2}=\sqrt{39}\). I'm trying to find the length now and I just want some confirmation that what I'm doing is correct. I split triangle SVT with a line to divide it into two right triangles. Let the point where the the altitude intersects with the ST be X. The height of this triangle is \(\sqrt{39}\). From S to X, using the pythagorean thereom, SX=19. Then from X to T, we know XT is 5. So the length of ST is 24. Is this correct?