Right-Triangle Revision Worksheet
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Right-Triangle Revision Worksheet
Section A: Pythagoras’ Theorem
Success criteria: I can identify the hypotenuse, choose the correct formula, show working and round my answer correctly.
Reminder: a² + b² = c², where c is the hypotenuse. The hypotenuse is opposite the right angle.
Use a calculator in degree mode when needed. Round lengths to 1 decimal place and angles to the nearest degree unless stated otherwise.
Clearly labelled description: the 6 cm and 8 cm sides meet at the right angle.
Section B: Trigonometry
Reminder: SOHCAHTOA: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Use inverse trig for missing angles.
Identify the opposite, adjacent and hypotenuse before choosing a ratio.
Section C: Applications and Challenges
Draw a labelled right triangle for each problem. Include units in your final answer.
Challenge: Choose the method
Decide whether Pythagoras or trigonometry is more suitable. Explain your choice briefly.
Answer Key
1. c = √(6² + 8²) = 10.0 cm.
2. c = √(9² + 12²) = 15.0 m.
3. c = √(5.5² + 7.2²) = 9.1 cm.
4. Missing side = √(13² − 5²) = 12.0 cm.
5. Missing side = √(10² − 6²) = 8.0 m.
6. Missing side = √(17² − 8²) = 15.0 cm.
7. Opposite = 12 sin 35° = 6.9 cm.
8. Hypotenuse = 8 ÷ cos 42° = 10.8 m.
9. Adjacent = 7 ÷ tan 28° = 13.2 cm.
10. Adjacent = 15 cos 63° = 6.8 m.
11. θ = tan⁻¹(9 ÷ 12) = 37°.
12. θ = cos⁻¹(14 ÷ 20) = 46°.
13. θ = sin⁻¹(11 ÷ 18) = 38°.
14. θ = tan⁻¹(5 ÷ 9) = 29°.
15. Height = √(5² − 1.2²) = 4.8 m.
16. θ = sin⁻¹(1.5 ÷ 6) = 14°.
17. Height = 4.5 tan 38° = 3.5 m.
18. Distance = 30 ÷ tan 35° = 42.8 m.
19. Use trigonometry: θ = tan⁻¹(7 ÷ 4) = 60°.
20. Use Pythagoras: length = √(13² − 5²) = 12.0 cm.
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