Shown is a regular triangular prism ABCDA1B1C1D1, all edges are equal to each other. a) What is the degree measure

| April 9, 2021 | education

Shown is a regular triangular prism ABCDA1B1C1D1, all edges are equal to each other. a) What is the degree measure of the angle between lines BA1 and C1C? b) Is it true that the degree measure of the angle between the straight lines BA1 and AC = 90 degrees?

Diagonal BA1 lies in the plane of the lateral face ABB1A1. The projection of the lateral edge CC1 onto the plane ABB1A1 is the lateral edge AA1, since all the lateral edges are squares.

Then the linear angle АА1В is the angle between the straight lines BA1 and C1C.

Since ABB1A1 is a square, the angle AA1B = 45.

An equilateral triangle lies at the base of the prism, since all the faces of the prism are equal, then all its internal angles are equal to 60.

The segment AB is the projection of the diagonal BA1 onto the plane ABC, and since the angle BAC = 60, then the angle between BA1 and AB is 60.

Answer: a) the angle between straight lines BA1 and C1C, b) is not correct.



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