GCSEMathsAQAHigherFlashcards4. Geometry & Measures3D Pythagoras & Trigonometry

3D Pythagoras & Trigonometry (AQA GCSE Maths)

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How can 3D problems involving Pythagoras' theorem and trigonometry be made easier?
It is usually easier to solve 3D Pythagoras' theorem and trigonometry problems by splitting them into 2D problems. Look for right-angled triangles that share a side or an angle with the information that you know or that you want to know.
State the 3D version of the Pythagoras' theorem formula.
The 3D version of Pythagoras' theorem is $d^{2} = x^{2} + y^{2} + z^{2}$
Where:
- $d$ is the straight line distance between two points
- $x$ is the distance in the $x$ -direction between the two points
- $y$ is the distance in the $y$ -direction between the two points
- $z$ is the distance in the $z$ -direction between the two points
How can you find the angle between a line and a plane?
Draw a new line from a point on the line creating a right-angled triangle. The angle between the line and the plane is the same as the angle between the initial line and the side of the triangle that lies on the plane.