; ] joins two opposite corners of a 3D shape, passing through the inside of the solid.","back":"A space diagonal joins two opposite corners of a 3D shape, passing through the inside of the solid.","points":null},{"id":"174b45ce-3520-4fc3-b781-73624efd8245","cardType":"basic","front":"What is the 2-step strategy for finding a cuboid's space diagonal without using the shortcut formula?","back":"

Find the face/base diagonal using Pythagoras.
Use that diagonal and the height in a second Pythagoras calculation.

","points":2},{"id":"b33983bb-c836-4990-9821-bb3e8a526e20","cardType":"basic","front":"What is the shortcut formula for the space diagonal $d$ of a cuboid with length $l$, width $w$, and height $h$?","back":"$$d^2 = l^2 + w^2 + h^2$","points":1},{"id":"1b6a409d-6077-4056-a0c2-46da3f03fb29","cardType":"cloze","front":"To find a missing depth $x$ in a cuboid where the space diagonal $d$, width $w$, and height $h$ are known, the formula is $x^2 = \\text{[...]}$.","back":"To find a missing depth $x$ in a cuboid where the space diagonal $d$, width $w$, and height $h$ are known, the formula is $x^2 = \\boxed{d^2 - w^2 - h^2}$.","points":null},{"id":"87d75b75-32f9-4cd3-9b61-7ac126747fd6","cardType":"cloze","front":"Common mistake: calculating $d = l + w + h$ for a cuboid is wrong because Pythagoras works with squares of lengths, not [ ].","back":"Common mistake: calculating $d = l + w + h$ for a cuboid is wrong because Pythagoras works with squares of lengths, not lengths added directly.","points":null},{"id":"26ccd6d4-2e76-4d40-a51e-619e94000a74","cardType":"basic","front":"When finding the angle between a cuboid's diagonal and its base, what must be used as the adjacent side?","back":"The base diagonal (not just one edge of the base).","points":1},{"id":"1a262f96-e531-4d7d-aae8-7b098e029290","cardType":"cloze","front":"The [ ] of a line onto a plane is like its shadow on that plane.","back":"The projection of a line onto a plane is like its shadow on that plane.","points":null},{"id":"892c9721-5ccf-428e-a4bd-f592b3c6c7c6","cardType":"cloze","front":"The projection of a line onto a plane is like its [ ] on that plane.","back":"The projection of a line onto a plane is like its shadow on that plane.","points":null},{"id":"c8cf2adf-4f40-456c-8f7b-7305a52e25e6","cardType":"basic","front":"How is the angle between a line and a plane defined?","back":"The angle between the line and its projection on the plane.","points":1},{"id":"cbc9874a-c667-43ee-a7be-048da2261069","cardType":"basic","front":"How do you find the projection of a point onto a plane?","back":"Drop a perpendicular line from the point down to the plane.","points":1},{"id":"bb4b80f8-7cf5-4fbf-a3c7-dad353993cc8","cardType":"cloze","front":"In a symmetrical square-based pyramid, the vertical height meets the base at the [ ] of the square.","back":"In a symmetrical square-based pyramid, the vertical height meets the base at the centre of the square.","points":null},{"id":"d3726a65-b803-48eb-af3f-34460b80aed1","cardType":"basic","front":"In a pyramid, what is the difference between vertical height and a sloping edge?","back":"

Vertical height goes straight from apex to base at 90 degrees.
Sloping edge connects the apex to a corner of the base.

","points":2},{"id":"ed75936b-b4df-4100-b9fe-31995b924e04","cardType":"basic","front":"In a squa

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards