What is the radius of the unknown planet?

Question

You are on a pleasure cruise through the universe and you crash in the ocean of an unknown planet. Your spaceship floats on the water and its top is 21 feet above the surface of the water. You swim away from the spaceship until you see its top on the horizon. Your laser range meter tells you that your eyes are 3 miles away from the top of the space ship. (You are a capable - if reckless and curious - swimmer.) The radius of the unknown planet is __________ miles.

Answer 1

Draw and label a diagram!

Label your position U

Label top of ship T

Label location of ship S

Label diameter SE, this is also the secant

5280² = 21(TE)

27878400 = 21(SE + 21)

27878400 = 21SE + 441

27877959 = 21SE

1327521.857 = SE (in feet)

251.4345942 = SE (in miles)

125.7122971 miles is the radius of the planet