It is known that the angle between line AB and plane a is 30 degrees, the angle between line AC and plane a is 6O degrees, ab = 6cm, AC = 8cm, and the projective ab 'and AC' of oblique line AB and AC in plane a are perpendicular to each other?

It is known that the angle between line AB and plane a is 30 degrees, the angle between line AC and plane a is 6O degrees, ab = 6cm, AC = 8cm, and the projective ab 'and AC' of oblique line AB and AC in plane a are perpendicular to each other?

The projection of a in plane α is a '
The angle between AB and plane α is 30 degrees, B is oblique foot, ab = 6cm,
∴A'B=3√3,
Similarly, a'c = 4,
A'B ⊥ a'c,
∴BC=√(27+16)=√43cm.

How many straight lines are there that a and B are on the plane α, and the angle of a and B is 40?, passing through a point outside α, a and a and B are at an angle of 30?
If it's convenient, can you draw the picture below?

Make the bisector of the angle between the straight line a and B in the plane. The angle between the bisector and a and B is 20 ° or 70 ° respectively. When the bisector rises around the intersection, the angle between the bisector and a and B is still equal, but it is increasing. Therefore, one bisector can turn to the position of 30 ° with a and B (two directions, two lines)

Line L belongs to plane 1. How many lines are there that pass through a point outside plane 1 and form an angle of 30 degrees with L and plane 1?

Because there are two planes that satisfy the conditions, there are countless planes in the plane, and the angle between the two planes is 30 degrees

The original slope with a length of 1km and an inclination angle of 45 degrees is to be reduced to 30 degrees, and then the slope length will be changed to?

1*cos45=√2/2km
(√2/2)/cos30=√6/3km