Some birds fly more slowly over water than over land. A bird flies at constant rate of 6 km/h over water and 10 km/h over land. To minimize the total flying time between the shore of one island and its nest, the bird will chose a path similar to the one represented in the diagram below. Given the measurements in the diagram, write the total time to fly from the island to the nest, as a function of the angle a between the direct line from one shore to the other and the flying line. Use optimization techniques to find the angle of flight that will ensure the shortest amount of time necessary for the bird to fly from the island to the nest.

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