Why does the base matter to calculate the area of a right triangle?
Can someone please explain how we got the central angle as 72 degrees in the regular pentagon inscribed in the circle?
What do you think the angle between the top point and B is, and the same for A?
angle A and angle B would be 108 degrees, right? and the central angle has to be the double of that?
No. Think about it this way: we have five angles that add up to 360 degrees (i.e, a full circle). This is not the interior angle of the polygon.
I didn’t get this at first either, but after rewatching the video I understand what Greg meant. He was not referring to the angle at the tip of each figure, but rather the inner angles that form when you divide the Equilateral Triangle and the Pentagon in triangles
You can get the Inner Angle of each triangle formed inside the Equilateral Triangle from the Center by doing 360/3 = 120°. If you look at it as a Sector between the top tip of the Equilateral Triangle and point B, this Sector’s angle is 120°.
Now if you divide the Pentagon in triangles, you can get the inner angle of each triangle from the Center by doing 360/5 = 72°. If you also look at this as a Sector between the top tip of the Equilateral Triangle and point A, this Sector’s angle is 72°
So, if you take the angle of the Big Sector Tip-B (120°) and substract the angle of the Small Sector Tip-A (72°) you get the angle of the Sector A-B = 120 - 72 = 48°. Knowing the angle and the radius of the Circle, you can now calculate Arc A-B
Hope I made that clear enough and it can help someone else. I found it much more simple to look at them as sectors, as you can get confused with the inner figures and how they relate to the arc 