A typical trigonometry problem is: If the bottom of a ladder leaning against a building is 15 feet from the base of the building and forms a 45-degree angle with the ground, how tall is the ladder? Another example involves a ramp that is 40 feet long and set at a 20-degree angle of inclination. How high off the ground is someone who walks to the end of the ramp?
The flagpole problem provides the height of a flagpole and the length of its shadow. For example, if a flagpole is 18 feet high and casts a shadow of 24 feet, what is the distance from the end of the shadow to the top of the flagpole? What is the angle between the line representing this distance and the shadow?
Trigonometry word problems describe objects that form a triangle, provide measurements and ask for the missing information. Solving the problem usually involves making a drawing and using a trigonometry function.
A more difficult trigonometry word problem involves an airborne object, a vehicle on the ground and two angles of elevation, and then asks for the speed or distance the vehicle traveled. For example, a hot-air balloon is hovering 800 feet above a road. A truck driver sees the balloon at an angle of 20 degrees. After 30 seconds of driving, the truck driver sees the balloon at an angle of 65 degrees. How far did the truck travel and how fast was it moving?