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3D Pythagoras & Trigonometry (Cambridge (CIE) IGCSE Maths)

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  • Front3D Pythagoras & Trigonometry

    How can 3D problems involving Pythagoras' theorem and trigonometry be made easier?

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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.

    A triangular prism with two right-angled triangles highlighted inside it.

  • State the 3D version of the Pythagoras' theorem formula.

    The 3D version of Pythagoras' theorem is d squared equals x squared plus y squared plus z squared

    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.

    Diagram showing the angle between a line and a plane.
Previous:Sine, Cosine Rule & Area of TrianglesNext:Trigonometric Graphs & Equations

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation