3 Dimensional Trigonometry


Drag the red dot to change the position of A.

The distance from a point A to a line BC is the length of the perpendicular from the point A to the line BC.

The angle between a line AD and a plane BCDE is the angle between AD and its projection on BCDE.

The angle between 2 planes ABC and BCDE is the angle APQ, where P is the point on the common line BC such that both AP & PQ are perpendicular to BC.





Exercises for students
Distance from a Point to a Line:
Move the point A so that it lies above the point B. What is the distance from A to the line BC?
Move A so that it lies above the point C. What is the distance from A to the line BC?
Move A anywhere. What is the distance from A to the line?
Rotate the line BC. What is the distance from A to the line?

Angle between a Line & a Plane:
Move A so that it lies above the point B. Where is the angle between AD & the plane BCDE?
Move A so that it lies above C. Where is the angle between AD & the plane BCDE?
Move A so that it lies above E. Where is the angle between AD & the plane?
Move A anywhere. Where is the angle between AD & the plane?
Rotate the plane BCDE. Where is the angle between AD & the plane?

Angle between 2 Planes:
Move A anywhere. Where is the angle between the planes ABC & BCDE?
Is the angle always at the mid-point of BC?
Move A so that it lies above the point E. Where is the angle between the planes ABC & BCDE?
Move A so that it lies above D. Where is the angle between the 2 planes?
Rotate the plane BCDE. Where is the angle between the 2 planes?




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