Finding Missing Angles Using SOHCAHTOA

This page focuses on using SOHCAHTOA to find missing angles in right-angled triangles. It explains the process of using inverse trigonometric functions to calculate unknown angles.

The steps for finding missing angles are:

1. Label the given lengths as O, A, or H
2. Determine which trigonometric ratio to use based on the given information
3. Set up the equation using the appropriate ratio
4. Use the inverse trigonometric function to solve for the angle

Highlight: To find an angle, we use inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹.

The page provides examples for each trigonometric ratio:

1. Using sine:

   Example: If O = 8.4 and H = 10.8, then θ = sin⁻¹(8.4 ÷ 10.8) ≈ 51.1° (3 sf)

2. Using cosine:

   Example: If A = 12 and H = 14.19, then θ = cos⁻¹(12 ÷ 14.19) ≈ 32.3° (3 sf)

3. Using tangent:

   Example: If O = 11.2 and A = 7.8, then θ = tan⁻¹(11.2 ÷ 7.8) ≈ 55.1° (3 sf)

Vocabulary: Inverse trigonometric functions (also called arcfunctions):

• sin⁻¹ or arcsin
• cos⁻¹ or arccos
• tan⁻¹ or arctan

The page also provides guidance on using a calculator for these inverse functions, typically accessed through the 'shift' or 'inverse' button followed by the regular trigonometric function key.

Highlight: Always remember to use the appropriate units (degrees or radians) and round your answers to a suitable number of significant figures or decimal places as required by the question.

SOH CAH TOA: Finding Missing Lengths and Angles

This page introduces the fundamental concept of SOHCAHTOA and its application in solving right-angled triangle problems. It covers the basics of finding missing lengths using trigonometric ratios.

Definition: SOHCAHTOA is a mnemonic device used to remember the ratios in trigonometry for sine, cosine, and tangent.

The page explains how to label the sides of a right-angled triangle:

• Opposite (O): The side opposite to the angle in question
• Adjacent (A): The side next to the angle in question
• Hypotenuse (H): The longest side, always opposite the right angle

Highlight: The hypotenuse is always the diagonal and opposite the right angle.

To find missing lengths, the process involves:

1. Labeling the given side and the side you need to find (O, A, or H)
2. Choosing the appropriate trigonometric ratio (sine, cosine, or tangent)
3. Applying the formula and solving for the unknown side

Example: To find H when O and the angle are given, use H = O ÷ sin θ. For instance, if O = 10.2 and θ = 64°, then H = 10.2 ÷ sin(64) ≈ 11.3 cm (3 sf).

The page also provides examples for finding the adjacent side using cosine and the opposite side using tangent.

Vocabulary:

• SOH: Sine = Opposite ÷ Hypotenuse
• CAH: Cosine = Adjacent ÷ Hypotenuse
• TOA: Tangent = Opposite ÷ Adjacent