John is a lighthouse manager, he needs to find out how tall the lighthouse is. He is standing 80 feet away looking at the lighthouse at an angle of 45°. He knows that 80 x cos(45) = 56. So the lighthouse is 56 feet tall.
One part of Johns job is that he needs to know how far away boats are from the lighthouses. He knows that the lighthouse is 56 feet tall and at a 55° angle. Therefore he knows that 56/tan(55) = 39. So that means that the boat is 39 feet away.
John had just noticed a plane wreak, He knows that he is 56 feet tall and that the plane is 160 feet away he needs to find the angle which it is at.
So he does tan^-1 160/56 = 70. So that means that the angle is 70 degrees
John then called in and reported where the wreck was located and went to go help the passengers.