This study notes covers Worked Example: Space Diagonal of a Cuboid within 3D Trigonometry for GCSE Mathematics. Revise 3D Trigonometry in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 2 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 4 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example: Space Diagonal of a Cuboid
A cuboid has dimensions 3cm × 4cm × 5cm. Find the length of the space diagonal.
Step 1 Find the base diagonal first
Base diagonal² = 3² + 4² = 9 + 16 = 25
Base diagonal = 5 cm
Step 2 Use base diagonal and height for space diagonal
Space diagonal² = 5² + 5² = 25 + 25 = 50
Space diagonal = √50 = 5√2 ≈ 7.07 cm
Practice questions for 3D Trigonometry
To find the angle between a line and a horizontal plane in a 3D problem, which technique is typically used?
Describe the general method for finding the angle between a line and a plane in a 3D problem.