Mel is designing a triathlon course, which will have three legs in the following order: biking, swimming,and running. She decides to make a course in the shape of a right triangle, with the hypotenuse as a3 kilometer swim down a straight stretch of the Charles River. Two possibilities are shown below.Mel knows the average triathlete swims at 2 km/hr, runs at 12 km/hr and bikes at 123 km/hr. Inorder to make her triathlon a real challenge, Mel wants to maximize the time it takes for an averagetriathlete to complete the course. In this problem, you'll help Mel by expressing this time as a functionof one variable.

(a) Express the amount of time it takes for an average triathlete to complete the course as a functionof, the angle between the running and swimming legs.

(b) What is the domain of the function you wrote in (a)?

(c) Express the amount of time it takes for an average triathlete to complete the course as a functionof the length of the biking leg

(d) What is the domain of the function you wrote in (c)?