This was always my favorite type of math problem, no huge shortcuts, just a lot of calculation to get a logical conclusion Worth noting that you didn't have to learn 30 60 90 triangles or do any trig at all for this problem--you already have the hypotenuse so you can just do the pythagorean theorem real fast in your head. c^2 - a^2 = b^2 so b = sqrt(3/4) or sqrt(3)/2. If you have your basic triangles super memorized already, cool, but if you don't, it's sometimes faster to just quickly calculate it out in the hyper-reliable way than to take even 5 seconds to try to verify in your head that a 30 60 90 triangle has certain ratios to their legs. Of course, if you weren't given the hypotenuse, it would indeed be critical to remember your triangles.
This was always my favorite type of math problem, no huge shortcuts, just a lot of calculation to get a logical conclusion
Worth noting that you didn't have to learn 30 60 90 triangles or do any trig at all for this problem--you already have the hypotenuse so you can just do the pythagorean theorem real fast in your head. c^2 - a^2 = b^2 so b = sqrt(3/4) or sqrt(3)/2. If you have your basic triangles super memorized already, cool, but if you don't, it's sometimes faster to just quickly calculate it out in the hyper-reliable way than to take even 5 seconds to try to verify in your head that a 30 60 90 triangle has certain ratios to their legs.
Of course, if you weren't given the hypotenuse, it would indeed be critical to remember your triangles.
i just integrated
0.5 * pi * r^2 - 2 * Integration of sqrt(1-x^2) from sqrt(3)/2 to 1
you should do some more programming videos
Hey can I do math with you