Missing angles
Objective. Use inverse trigonometric functions with appropriate accuracy.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Missing angles are calculated using inverse trigonometric functions once two sides of a right-angled triangle are known. Form the ratio from the two known sides (e.g. opposite/hypotenuse), then apply sin⁻¹, cos⁻¹ or tan⁻¹ to that decimal to recover the angle. For example, if opposite = 5 and hypotenuse = 10, sin θ = 0.5, so θ = sin⁻¹(0.5) = 30°. Always round the final angle sensibly, usually to 1 decimal place, and check it's less than 90° for a right-angled triangle.
Worked example
A right-angled triangle has opposite side 7 cm and hypotenuse 12 cm. Find the missing angle θ to 1 decimal place.
- 1sin θ = opposite/hypotenuse = 7/12
- 27/12 ≈ 0.5833
- 3θ = sin⁻¹(0.5833)
- 4θ ≈ 35.7°
Answer: 35.7°
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Start practisingCommon mistake. Students sometimes apply sin⁻¹ directly to a side length rather than to the ratio of two sides; always divide the sides to get a decimal between 0 and 1 before using the inverse function.
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