
Find the closest point on the triangle to the center of the sphere, and then see if it's inside the radius of the sphere.
In other words, find the distance of every triangle vertex to the sphere center. If distance < radius then true. You can and should use the (square_distance < square_radius) to avoid the Square Root.
This is a simple yes or no, it won't give you how or where it hit the sphere.
Also it may not work if any of the objects is moving (tri or Sphere), if the velocity (speed) is to great or if the time step is long, making possible to miss the collision.
NOTE: But there are a bunch of articles/tutorials on this subject already, make a search for it, including here on Flipcode.
