Draw a diagram for each problem and answer the question in context. Do not forget to include the units.
1) A plane is 10,000 feet above the ground and is getting ready to land at an airport soon. The plane is descending at an angle of depression of 15 degrees. Calculate the horizontal distance between the plane and the airport, and the distance the plane still has to travel before it lands.
2) A plane sees another plane whose altitude is 12,000 feet below it. The angle of depression of 12 degrees. Calculate the horizontal distance between the two planes as well as the distance between them.
3) A person that is 5.5 feet tall (at eye level) is looking up at a tree at an angle of elevation of 35 degrees. The person is 25 feet away from the tree. Calculate the height of the tree.
Provide diagrams and detailed solutions.