Sam is an astronomer on planet hua, which orbits the distant star barnard. it has recently been accepted that hua is spherical in shape, although its exact size is unknown. while studying in the library, in the city of joy, sam learns that during equinox, barnard is directly overhead in the city of bar, located 1100.0 km north of his location. on the equinox, sam goes outside and measures the altitude of barnard at 67 degrees. what is the radius of hua in km?