?","back":"A line that goes through the inside of a 3D shape from one corner to the opposite corner.","points":1},{"id":"a4c8ea31-b43a-4e25-8f62-f87e0df09967","cardType":"cloze","front":"For a cuboid with perpendicular edges $l$, $w$, and $h$, the space diagonal $d$ can be found using the formula: $\\text{[...]}$.","back":"For a cuboid with perpendicular edges $l$, $w$, and $h$, the space diagonal $d$ can be found using the formula: $\\boxed{d^2 = l^2 + w^2 + h^2}$.","points":null},{"id":"0efa8335-7b79-4c8d-88fc-f8c3f3511480","cardType":"basic","front":"When calculating the space diagonal of a cuboid without the shortcut, which two steps are required?","back":"

Use Pythagoras on the base to find the face diagonal.
Use Pythagoras with the face diagonal and the vertical height.

","points":2},{"id":"bf3a3cf3-3128-431b-a1e1-6bffb3be89cf","cardType":"basic","front":"If you are given the space diagonal and two edge lengths of a cuboid, how do you find the third edge length?","back":"Subtract the squares of the known edges from the square of the space diagonal: $a^2 = d^2 - b^2 - c^2$.","points":2},{"id":"ca2c7b79-f672-4832-a2c1-07cf8ee4263e","cardType":"basic","front":"In angle notation (e.g. angle $ECA$), which letter indicates the vertex where the angle is measured?","back":"The middle letter (in this case, $C$).","points":1},{"id":"b842f77a-3919-458b-afb4-3847a18e7f37","cardType":"cloze","front":"The angle between a line and a plane is defined as the angle between the line and its [ ] on that plane.","back":"The angle between a line and a plane is defined as the angle between the line and its projection on that plane.","points":null},{"id":"5d191da0-b127-485d-a0bf-478aedbdc599","cardType":"basic","front":"How is the projection of a line onto a flat plane described?","back":"It is the \"shadow\" of the line dropped straight down (perpendicularly) onto the surface.","points":1},{"id":"84fc6e1f-255c-4d64-8c57-a425ac2daaeb","cardType":"basic","front":"In a square-based pyramid, where does the vertical height meet the base?","back":"At the centre of the square base, where the base diagonals intersect.","points":1},{"id":"e6803990-e6b4-475c-bc47-2bb736cd3438","cardType":"basic","front":"How do you calculate the distance from a corner of a square-based pyramid to the centre of its base?","back":"Find the length of the base diagonal using Pythagoras, then halve it.","points":2},{"id":"5ae4329e-d5d6-4bba-adb7-54caf0350940","cardType":"cloze","front":"The formula for the volume of a pyramid is $$\\text{[...]}$$.","back":"The formula for the volume of a pyramid is $$\\boxed{V = \\frac{1}{3} \\times \\text{base area} \\times \\text{vertical height}}$$.","points":null},{"id":"cdf9aacb-e36a-4504-859b-73f7dc373356","cardType":"basic","front":"Which trigonometric ratio should be used if you know the side opposite an angle and the adjacent side?","back":"Tangent ($\\tan\\theta = \\frac{O}{A}$).","points":1},{"id":"6db49dc8-bea8-4fc6-8950-da8ce89d4c2c","cardType":"cloze","front":"In a right-angled triangle, the [ ] is always the side opposite the $90^\\circ$ angle.","back":"In a right-angled triangle, the hypotenuse is always the side opposite the $90^\\circ$ angle.","points":null},{"id":"a1635ef1-2681-41a8-9f91-ec3ecc7d9ac3","cardType":"cloze","front":"To find the angle $\\theta$ when the opposite and hypotenuse are known, use the formula $\\text{[...]}$.","back":"To find the angle $\\theta$ when the opposite and hypotenuse are known, use the formula $\\boxed{\\sin\\theta = \\frac{\\text{opposite}}{\\text{hypotenuse}}}$.","points":null},{"id":"a394c2fc-952d-4

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards

3d Pythagoras and Trigonometry Flashcards