20.5 3D Pythagoras and trigonometry — Practise
Work independently. Estimate where useful, show your method, and check units. In the mixed questions, choose the method and give a reason.
- H A cuboid measures 3 cm, 4 cm and 12 cm. Find its space diagonal.
- H A cuboid measures 5 cm, 12 cm and 9 cm. Find its space diagonal to 3 significant figures.
- H A cuboid has base dimensions 6 cm by 8 cm and height 10 cm. Find the space diagonal.
- H A cuboid has a 5 cm by 12 cm base and height 8 cm. Find the angle between its space diagonal and base to 1 decimal place.
- H A cube has side 4 cm. Find its space diagonal exactly.
- H A cuboid is 4 m by 7 m by 24 m. Find its space diagonal.
- H A cuboid is 9 cm by 12 cm by 20 cm. Find the space diagonal to 1 decimal place.
- H A cube has side 6 cm. Find the angle between the space diagonal and a face diagonal to 1 decimal place.
Answers and concise solutions
1. Question 1
Answer: 13 cm
2. Question 2
Answer: 15.8 cm
3. Question 3
Answer: 10√2 cm
4. Question 4
Answer: 31.6°
5. Question 5
Answer: 4√3 cm
6. Question 6
Answer: √641 m
7. Question 7
Answer: 25.0 cm
8. Question 8
Answer: 35.3°