My Favorite Math Problem
Right Angle Trigonometry Problem
I created a Right Angle Trigonometry math problem called Swimming at Sea. I also created a diagram to help students visualize the problem. There are three parts to the problem. You can find both hints and solutions by clicking on the links at the bottom of this page.
Part A:
Brian is in a lighthouse perched on a cliff. The lighthouse is 85 feet tall, and the cliff is 100 feet above sea level. His job is to observe the swimmers in the water. There is a buoy with an angle of depression of 63°. He can also see a swimmer at sea with an angle of depression of 35°. How far away is the swimmer from the buoy? (Round to the nearest tenth of a foot)
Part B:
There is a waterfall out at sea, and it is determined that after 300 feet from the cliff it is not safe to continue on. At what angle will Brian have to alert the swimmer to turn around? (Round to the nearest degree)
Part C:
If on a given day, the sea level rises 20 feet, does the angle at which Brian must alert the swimmer change? If so, what is the new angle? (Round to the nearest degree)
Hints
Solution