sam is an astronomer

Question

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 1300.0 km north of his location. On the equinox, Sam goes outside and measures the altitude of Barnard at 74 degrees. What is the radius of Hua in km?

Answer 1

Directly overhead is 90 degrees. 1300.0 km south at Sam's location Barnard is at 74 degrees. The difference 90 - 74 = 16 degrees is the portion of the 360 degree circle that represents the circumference of Hua. So 1300.0 km is 16 / 360 of the circumference = 0.044 x circumference. Circumference = 1300 / 0.044 = 29,250 km. The equation for circumference is 2π x radius. So 2πr = 29250 and radius of Hua = 4655.3 km.