Page 1: Calculating Distances Using Trigonometry

This page introduces fundamental concepts of trigonometry in right triangles and demonstrates how to calculate distances using trigonometric ratios.

Definition: A right triangle contains three sides (adjacent, opposite, and hypotenuse) and three angles, with one angle always being 90 degrees.

Vocabulary:

• Hypotenuse: The longest side of a right triangle, opposite to the right angle
• Adjacent: The side next to the angle being considered
• Opposite: The side across from the angle being considered

Example: In a right triangle ABC with angle ABC = 40°, using cos(ABC) = Adjacent/Hypotenuse, we can calculate AB = 2.3m.

Highlight: The three main trigonometric ratios are:

• sin(θ) = opposite/hypotenuse
• cos(θ) = adjacent/hypotenuse
• tan(θ) = opposite/adjacent

Page 2: Determining Angles Using Trigonometric Ratios

This page focuses on finding angle measurements using known trigonometric values and side lengths in right triangles.

Example: In a right triangle ABC with sides 3.6 and 4.5, we can determine angle BAC using cos(BAC) = 3.6/4.5 = 0.8.

Highlight: When solving for angles:

1. Identify the known sides and their relationship to the angle
2. Select the appropriate trigonometric ratio
3. Use inverse trigonometric functions to find the angle

Definition: The inverse trigonometric functions (arcsin, arccos, arctan) are used to find angles when trigonometric ratios are known.

Vocabulary:

• Inverse trigonometric functions: Mathematical operations that "undo" trigonometric functions to find angles
• Arc length: The length of a curved line segment that is part of a circle