Two ships leave the same dock at noon. The angle between the ships when they left the dock was 16 ∘ and remains constant. If one ship travels at a rate of 13 km/hr and and the other ship travels at a rate of 17 km/h. Find the rate at which the distance between the two ships is changing when it's 5:00 pm. Express your answer in km/hr.

Answer:   5.76 km/hStep-by-step explanation:After the first hour, the ships are 5.76 km apart. That separation rate remains constant since the speed and direction of each ship remains constant.Distance between the ships is increasing at 5.76 km/h.___A triangle solver is a useful tool for this. The Law of Cosines can also be used to find the distance between the ships after 1 hour.   c² = a² + b² - 2ab·cos(C)   c² = 13² +17² -2·13·17·cos(16°) ≈ 33.1223   c ≈ √33.1223 ≈ 5.755 . . . . kmThe distances are all proportional to time. The separation distance increases each hour at the same rate it did in the first hour:   5.76 km/h