In a regular quadrangular pyramid SABCD, all edges are equal to 1. Find the distance between lines AS and DC.
| May 2, 2021 | education
Consider a triangle SCD, where SH is the distance between AS and DC.
It is also known that SC = SD = 1, SН – height, which is the bisector and median.
It is also known that DH = 0.5.
It is necessary to consider the triangle SНD, in which the angle Н = 90 °.
We will use the Pythagorean theorem: 1 = 0.25 + (SH) 2,
SH = √0.75.
Answer: SH = √0.75.
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