Finding Missing Sides Using Trigonometry

This page demonstrates how to solve trigonometric equations with sin and cos to find missing sides in a right-angled triangle.

Example: To find the opposite side $x$ in a triangle with hypotenuse 12m and angle 35°:

1. Identify the given information: angle = 35°, hypotenuse = 12m
2. Choose the appropriate formula: Sin θ = Opposite / Hypotenuse
3. Set up the equation: Sin 35° = x / 12
4. Solve for x: x = 12 × Sin 35° = 6.88 (rounded)

Highlight: When solving for a side, multiply if the known side is in the denominator of the ratio, and divide if it's in the numerator.

Using Tangent to Find Missing Sides

This section explains how to solve trigonometric ratios using the tangent function to find missing sides in a right-angled triangle.

Example: To find the adjacent side $x$ in a triangle with opposite side 15m and angle 18°:

1. Identify the given information: angle = 18°, opposite = 15m
2. Choose the appropriate formula: Tan θ = Opposite / Adjacent
3. Set up the equation: Tan 18° = 15 / x
4. Solve for x: x = 15 / Tan 18° = 13.51 (rounded)

Highlight: When solving for the adjacent side using tangent, divide the opposite side by the tangent of the angle.

Finding Missing Angles in Trigonometry

This page covers how to solve trigonometric equations to find missing angles in a right-angled triangle.

Steps to find a missing angle:

1. Label the sides of the triangle
2. Identify the known sides
3. Choose the appropriate trigonometric ratio
4. Set up the equation and solve for the angle using inverse trigonometric functions

Example: To find angle x in a triangle with adjacent side 3cm and hypotenuse 8cm:

1. Identify the given information: adjacent = 3cm, hypotenuse = 8cm
2. Choose the appropriate formula: Cos x = Adjacent / Hypotenuse
3. Set up the equation: Cos x = 3 / 8
4. Solve for x using inverse cosine: x = Cos⁻¹$3/8$ = 67.98° (rounded)

Highlight: Use a calculator to solve trigonometric equations involving inverse functions like Cos⁻¹, Sin⁻¹, or Tan⁻¹.

Introduction to Trigonometry

Trigonometry is the study of relationships between angles and sides in right-angled triangles. This page introduces the fundamental concepts and steps for solving trigonometry problems easily.

The three main steps to solve trigonometric problems are:

1. Label the triangle
2. Pick the correct formula
3. Set up and solve the equation

Vocabulary:

• Hypotenuse: The longest side of a right-angled triangle, opposite the right angle
• Opposite: The side opposite to the angle in question
• Adjacent: The side next to the angle in question

Definition: SOH CAH TOA is a mnemonic device used to remember the trigonometric ratios:

• Sin θ = Opposite / Hypotenuse
• Cos θ = Adjacent / Hypotenuse
• Tan θ = Opposite / Adjacent

Highlight: Trigonometry is used to calculate missing sides or angles in right-angled triangles.