Sounds like you're talking about the main lobe of a radio antenna.
It's kind of sloppy to say that the "max" extends across some width, since the "max"
only happens in one single, specific direction.
The "beam-width" is also often referred to as the "3dB beam-width". It's the angle between
the two points where the power is 3 dB less than the max ... one point on each side of the max.
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The conduction angle in an SCR is the phase angle relative to the power line at which point the gate is fired to commit the anode to conduct to the cathode. By varying the conduction angle, you can change the average power transferred by the SCR.
The theorem you are referring to is a2+b2=c2 which is called the Pythagorean theorem. This describes the side lengths of a right triangle in which the two sides that meet at a right angle are sides a and b respectively and side c is the hypotenuse.
It is called the "exponent".
Power
You mean a power polygon right? I'm going to assume you do since poluyon isin another language that I don't know... You use a protractor, like you do withnormal polygons... but they are used more as a tool to learn what is obtuseand acute angles are that the angle itself...And for those who don't know what a power polygon is check this out: What_is_a_power_polygon