Solve the right triangle completely.
To begin, notice that two angles are known — and The third angle can be found using the Interior Angles Theorem. Thus, the third angle measures
Right triangles can be used to solve problems in context. Sometimes, it can be helpful to use angles of elevation or angles of depression.
Suppose someone is standing on the ground looking up toward the top of a tree. The angle made between the horizon and the viewer's gaze as they look up is an angle of elevation.
Suppose someone is standing on a cliff looking down toward a ship in the ocean below. The angle made between the horizon and the viewer's gaze as they look down is an angle of depression.
Martina is sitting on a bench in a harbor. A sail boat lies meters away from her. On top of the boat's meter high mast there is a seagull. Find the angle of elevation and depression when Martina and the seagull look at each other.
To begin, we can make a sketch to help us visualize the situation. Martina is labeled the boat and the seagull
The angle of elevation, is the angle looking up from the horizon. Since the seagull is higher than Martina, will be the angle made when Martina looks up toward the seagull. Let's add this line to the diagram.
Notice that the two horizont lines are parallel and that the line of sight is a transversal. By the Alternate Interior Angles Theorem and are congruent. Therefore, the angle of depression is also approximately