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.