Is the Angle A'ô'B' Always 90 Degrees in a Special Case?

In summary, the theorem of projection states that a right angle can be projected orthogonally onto a plane if one of its sides is parallel or contained within the plane (reference pic 1). However, in a specific case where one of the two lines is orthogonal to the plane P and the other is parallel, is the angle A'ô'B' still 90 degrees? (reference pic 2). The proof shows that in the triangle A'O'B', A'O' is equal to A'B' (therefore isosceles) and O'Â'B' is equal to 0 degrees, making A'ô'B' equal to 90 degrees. However, if one side is parallel and the other is orthogonal,
  • #1
Sabine
43
0
le theoreme de projection. un angle droit se projette orthogonalement sur un plan suivant un angle droit si un de ses cotes est parallele a ce plan ou contenu dans ce plan (reference pic 1).

mais si on pend un cas particulier dans lequel une de ses 2 droites est othogonale au plan P et l'autre est parallele alors l'angle A'ô'B' est-t-il encore 90 degre? (reference pic 2)


demonstartion dans le triangle A'O'B' on a
A'O'=A'B' (donc isocele)
O'Â'B'= 0 degre
d'ou A'ô'B' = 90 degre
 

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  • #2
Si un cote est parallele et l'autre orthogonal, alors l'angle projete sur le plan devrait etre 0 ?? ou alors : il n'y a qu'une seule demi-droite projetee en une demi-droite (celle parallele) l'autre devient un point, et donc on pourrait dire que la projection de l'angle n'est pas un angle dans ce cas precis?
 
  • #3
on ne peut pas dire que l'angle est zero d'apres le theoreme de la projection l'angle doit etre egal a 90 degre mais puisque c un angle entre une droite et un point j'ai essaye de demontrer que l'angle reste 0 degre (voir demonstration)
 

FAQ: Is the Angle A'ô'B' Always 90 Degrees in a Special Case?

1. What is "la direction d'un point"?

La direction d'un point refers to the angle or orientation at which a point is facing or moving in relation to a reference point or object.

2. How is "la direction d'un point" measured?

La direction d'un point is typically measured in degrees, with 0 degrees representing a point facing directly north and 180 degrees representing a point facing directly south.

3. What is the difference between "la direction d'un point" and "l'angle d'un point"?

While both terms refer to the orientation of a point, "la direction d'un point" specifically refers to the angle at which a point is facing or moving, while "l'angle d'un point" can refer to any angle formed by two lines or objects.

4. How can "la direction d'un point" be changed?

La direction d'un point can be changed by physically rotating the point or by changing the angle at which it is facing or moving.

5. Why is "la direction d'un point" important in science?

La direction d'un point is important in science because it allows us to describe the orientation of an object or point in space and to understand how it is moving or interacting with other objects. This information is crucial in fields such as physics, astronomy, and navigation.

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