Applying Trigonometry

This page delves into practical applications of trigonometry, demonstrating how to calculate sides and angles in triangles using trigonometric functions and the Pythagorean theorem.

The page is divided into several sections:

1. Determining Cosine, Tangent, and Sine
2. Calculating Sides
3. Calculating Angles

For calculating sides, two methods are presented:

1. Using the Pythagorean theorem (a² + b² = c²)
2. Using trigonometric functions (e.g., c = a • sin(angle))

Example: To find side c, use the formula c = a • sin(angle). For instance, if a = 6.8 and the angle is 29.5°, then c = 6.8 • sin(29.5°) = 3.35 cm.

For calculating angles, two scenarios are discussed:

1. When two angles are given (using the fact that angles in a triangle sum to 180°)
2. When one angle is sought (using inverse trigonometric functions)

Example: If two angles in a triangle are 30° and 90°, the third angle can be calculated as: 180° - (30° + 90°) = 60°.

The page also includes important reminders:

Highlight:

• The adjacent side is next to the angle being considered.
• The opposite side is across from the angle being considered.
• In trigonometry, we deal with side ratios in right-angled triangles.
• The longest side, opposite the right angle, is called the hypotenuse.
• The two shorter sides are called catheti (singular: cathetus).

These concepts are crucial for mastering Trigonometrie Dreieck Formeln and solving complex Trigonometrie Dreieck Aufgaben PDF.