Right-Angled Triangle Trigonometry

What is SOHCAHTOA?

• SOHCAHTOA is a mnemonic device to help remember the trigonometric ratios for right-angled triangles.

• It stands for:

  • Sine = Opposite / Hypotenuse

  • Cosine = Adjacent / Hypotenuse

  • Tangent = Opposite / Adjacent

Key Concepts

• Right-Angled Triangle: A triangle with one angle measuring 90 degrees (a right angle).

• Hypotenuse: The side opposite the right angle (always the longest side).

• Opposite Side: The side opposite the angle you are considering.

• Adjacent Side: The side next to the angle you are considering (not the hypotenuse).

Using SOHCAHTOA

1. Identify the angle: Determine which angle you are working with in the right triangle.

2. Label the sides: Label the sides of the triangle as hypotenuse, opposite, and adjacent relative to the chosen angle.

3. Choose the correct ratio: Select the appropriate trigonometric function (sine, cosine, or tangent) based on which sides are given or needed.

4. Substitute values: Substitute the known side lengths into the chosen ratio.

5. Solve for the unknown: Use algebraic methods to solve for the unknown side length or angle.

Example:

• If you know the angle and the hypotenuse, and need to find the length of the opposite side, you would use the sine function (SOH).

Applications

Right-angled triangle trigonometry has numerous applications in various fields, including:

• Physics: Calculating forces, velocities, and angles in projectile motion and other situations.

• Engineering: Designing structures, bridges, and other constructions.

• Navigation: Determining distances and directions in surveying and navigation.