how does an electric fan manage to throw so much air when it is switched on?

There is a triangle ABC.

Extend BA to point D, so DA = CA

Join CD

Angle ADC = ACD

Angle BCD ACD, so angle BCD ADC (or BDC)

So in triangle DCB, line DB (or DA + AB) BC

But line DA = AC, so lines AC + AB BC

When the fan is switched on, the motor starts whirling. It causes the blades to move which fastens the speed of the air present inside the room and throw the air in all direction.