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Flip to reveal answersHow do you find an angle in a 3D solid?
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All 8 Flashcards — Angles in 3D
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Question
How do you find an angle in a 3D solid?
Answer
Spot a right-angled triangle inside the solid and use SOH-CAH-TOA.
Question
How is the angle between a line and a plane defined?
Answer
The angle between the line and its projection (shadow) on the plane.
Question
What do you often need before the angle triangle is complete?
Answer
A face or base diagonal — found with Pythagoras.
Question
Face diagonal of an a × a square?
Answer
a√2 (= √(a² + a²)).
Question
Space diagonal of an a × a × a cube?
Answer
a√3 (= √(a² + a² + a²)).
Question
What's the 'angle in a semicircle' fact?
Answer
A diameter subtends a right angle (90°) at any point on the circle.
Question
Why redraw the triangle separately?
Answer
It's much easier to apply trig to a flat 2D triangle than to the 3D picture.
Question
Typical 3D problem structure?
Answer
Two steps: a length by Pythagoras, then an angle by trig.
Read the notes
Full study notes for Angles in 3D
Topic 3.1 hub
3D geometry
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Math AA SL exam skills
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