Arc length problem?????????

You land your spaceship on a spherical asteroid between Earth and Mars. Your copilot walks 1000 feet away along the asteroid's smooth surface carrying a 10 ft rod and thereby vanishes over the horizon. When she places one end of the rod on the ground and holds it straight up and down, you-- lying flat on the ground-- can just barely see the tip of the rod. Use the information to find the radius R of the asteroid in miles.