## Trigonometric Function Values of Special Angles

# Special Angles Evaluating Trigonometric Function Values & Word Problems

In this algebra lecture, I am going to discuss word problems involving special angles. In particular, I will solve problems involving angle of elevation and depression. Before we proceed with the problems, I will be deriving the trigonometric function values of these special angles – 30, 60 and 45 degrees.

- A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 30◦, how far offshore is the boat?
- Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 60◦, how far are you from the base of the plateau?
- Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 60◦, how far are you from the base of the plateau?
- The angle of depression of a vehicle from the top of a tower on the ground is 60. If the vehicle is away from the building at a distance of 100 meters, find the height of the tower.