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:
- Label the given lengths as O, A, or H
- Determine which trigonometric ratio to use based on the given information
- Set up the equation using the appropriate ratio
- 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:
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Using sine:
Example: If O = 8.4 and H = 10.8, then θ = sin⁻¹(8.4 ÷ 10.8) ≈ 51.1° (3 sf)
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Using cosine:
Example: If A = 12 and H = 14.19, then θ = cos⁻¹(12 ÷ 14.19) ≈ 32.3° (3 sf)
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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.
