A circular lake has a diameter of 10 miles. Mathman and several other contestant

Question

A circular lake has a diameter of 10 miles. Mathman and several other contestants are assembled at point A and need to get to point B in the shortest amount of time. The rules are that you can get into a boat and row in a straight line towards any point P on the circumference between A and B. You then get out of the boat and run along the remaining circumference until you get to point B. Each contestant can row a boat at 3 miles per hour and can run around the circumference of the lake at 5.5 miles per hour. After a few quick calculations Mathman climbs in his boat, heads in a direction that makes angle theta with diameter AB, gets out at point P and runs around the circumference to point B. To mathman's dismay, all the other contestants have arrived before him. Mathman then realzes that his calculations gave him the angle theta which made for the longest trip, not the shortest. What angle theta, to the nearest degree, did Mathman use?

Explanation / Answer

theta = 0 degrees

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