Since we have a right triangle you did well to think of the Pythagorean theorem.
Now, if we label the horizontal leg of the triangle , we know the vertical leg is fixed at 50 ft., and let's label the hypotenuse (the actual distance from the judge to the horse) as . let all linear measures be in feet and time be in seconds. So we have:
Let's let represent the angle subtended by the vertical leg and the hypotenuse.
Now, we are also told that when that and
Can you think of a way to relate to and the vertical leg?