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Little fool mathematics series; like ...
The first little question

draw

Draw by yourself

A triangle with p as its vertex.

Because PC

Vertical AB

So the triangular PCB is a right triangle.

Because the angle abp=45.

So the angle bpc=45.

Triangle packaging congruent triangles PCB(AC=BC

Angle ACP= Angle BCP = 90°.

PC=PC)

So the triangle PAC is also an isosceles right triangle.

So PC; Pa= 1: root number 2

The second small problem

Triangle packaging congruent triangles PCB(AC=BC

Angle ACP= Angle BCP = 90°.

PC=PC)

Because ab=ap

So pb=ap

So Pb; CB = 2; 1

So Sina angle BPC = 1/2.

So the angle bpc=30.