Flashcards · Maths · Further Trigonometry
Trigonometry in 3D and Mixed Problems
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What is the length of a space diagonal of a cuboid?
\(\sqrt{l^2 + w^2 + h^2}\).
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What is the base diagonal of a 4 cm by 3 cm rectangle?
5 cm.
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What is the angle between a line and a plane?
The angle between the line and its shadow on the plane.
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Where is the apex of a square-based pyramid?
Directly above the centre of the base.
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What is the length of the diagonal of a square with side 6 cm?
\(6\sqrt{2}\) cm.
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What do you do first in a 3D problem?
Draw a right-angled triangle on its own.
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What should you mark on the triangle?
The right angle and the known lengths.
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What does \(\tan\theta = 1\) mean?
\(\theta = 45^\circ\).
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Which trig ratio uses opposite and adjacent?
Tangent.
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Which rule is used if there is no right angle?
The sine rule or the cosine rule.
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What is \(\sqrt{48}\) in simplest form?
\(4\sqrt{3}\).
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Why keep surds until the end?
To give an exact answer and avoid rounding errors.
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What is \(\sin 30^\circ\)?
\(\dfrac{1}{2}\).
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What is the space diagonal of a cube with edge 1?
\(\sqrt{3}\).
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How many right-angled triangles are needed for a space diagonal?
Two.
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Is the space diagonal longer than the edges?
Yes.