[Math] Angle between slanting edges of pyramid P and its base confusion..


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What we normally do when we find the angle between a slanting edge and a pyramid is find angle PQE, or PAE.

But why is angle BAE $\neq$ PQE or PAE?

Line AB is also a side of a square base ABCD and AE is part of a slanting edge.
It seems odd to me. The angle must be the same?

Many thanks in advance

Best Answer

Imagine that the height of the pyramid is very small. Then $\angle PQE$ and $\angle PAE$ each go toward 0 (though not at the same rate), whereas $\angle BAE$ goes towards $45^\circ$.