Applications of Trigonometric Functions

Terminology

· Regular polygon (regular n-gon): An n-sided polygon where all sides have the same measure and all angles have the same measure.

· Central Angle: An angle formed by the line segments connecting consecutive vertices t the center of a regular

n-gon.

· Measure of the central angle of a regular n-gon =

Example 3: A circle has an inscribed regular hexagon. What is the area of the shaded region?

Terminology

· Angle of Elevation: Angle between the line of sight and the horizontal where an object is sighted above the horizontal.

· Angle of Depression: Angle between the line of sight and the horizontal where an object is sighted below the horizontal.

Example 5: An observer standing at the top of a 1000 foot hill observes the angle of depression to the base of the east side of the hill to be while the angle of depression to the west side of the hill is . How wide is the base of the hill?

Overhead 6.3,pg2

Right Triangle Definitions

Area of a Triangle:

· A = ½(base)(height)

· A = ½(a)(b), where a and b are the lengths of the sides on either side of the angle .

Similar Triangles

Two triangles are similar under any one of three conditions:

1. Two pairs of corresponding sides are proportional and their included angles are congruent. (SAS).

2. Two pairs of corresponding angles are congruent. (AA)

3. All three pairs of corresponding sides are proportional. (SSS)