Page 2: Finding Missing Angles in Right-Angled Triangles

This page expands on the concepts by demonstrating how to calculate missing angles using inverse trigonometric functions. Multiple examples showcase different scenarios and approaches.

Example: Finding a missing angle using tangent:

1. Given opposite = 12cm and adjacent = 13cm
2. Using tan(θ) = opposite/adjacent
3. θ = tan⁻¹(12/13)
4. Final answer: θ = 35.69°

Highlight: When calculating angles, remember to use inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) and ensure your calculator is in degree mode.

Definition: Inverse trigonometric functions (also called arc functions) allow us to find angles when we know the sides of a right-angled triangle.

Vocabulary: Arc functions - the inverse operations of trigonometric functions, written as sin⁻¹, cos⁻¹, or tan⁻¹ (also written as arcsin, arccos, arctan).

Page 1: Calculating Missing Sides in Right-Angled Triangles

This page introduces the fundamental concepts of calculating missing sides in right-angled triangles using trigonometric ratios. The content focuses on proper labeling and systematic problem-solving approaches.

Definition: A right-angled triangle contains three sides: the hypotenuse (longest side opposite the right angle), the opposite (side directly across from the angle in question), and the adjacent (side touching the angle in question).

Vocabulary: SOH CAH TOA - a mnemonic device representing the three main trigonometric ratios:

• Sine = Opposite/Hypotenuse
• Cosine = Adjacent/Hypotenuse
• Tangent = Opposite/Adjacent

Example: Finding a missing side using sine:

1. Given a 30° angle and hypotenuse of 25cm
2. Using sin(30°) = opposite/25
3. Solving for x: x = 25 × sin(30°)
4. Final answer: x = 12.53cm

Highlight: When solving for missing sides, always start by correctly labeling the triangle and identifying which trigonometric ratio to use based on the given information.