3D Trigonometry Flashcards

The use of trigonometry and Pythagoras' Theorem to solve problems involving three-dimensional shapes, such as cuboids, pyramids, and prisms.

Used to find the length of a diagonal in a 3D shape by applying Pythagoras' Theorem twice.

The length of the diagonal of a cuboid is \( \sqrt{l^2 + w^2 + h^2} \), where \( l \), \( w \), and \( h \) are the length, width, and height.

Use trigonometric ratios (sine, cosine, tangent) to calculate angles between edges or between an edge and a face in 3D shapes.

Sine, cosine, and tangent are used to relate angles and side lengths in right-angled triangles: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \), \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \), \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).

A triangle formed in a 3D shape where one angle is 90°. Trigonometry and Pythagoras' Theorem can be applied to solve problems.

To find the angle between a line and a plane, use trigonometry with the triangle formed by the line, its projection on the plane, and the perpendicular from the line to the plane.

1. Identify the right-angled triangle(s). 2. Use Pythagoras' Theorem to find missing lengths. 3. Use trigonometric ratios to find angles or other side lengths.

Common shapes include cuboids, pyramids, and triangular prisms. Problems often involve finding lengths or angles within these shapes.

Used in fields like architecture, engineering, and navigation to calculate distances, heights, and angles in three-dimensional spaces.