Preparation+for+25+August+2010+PM2+lesson

=﻿﻿﻿Hi guys, I am going to draft up a document for our presentation on Wednesday. Jia Wei, please post a summary of our (mostly your) findings so I can include it in. Meanwhile, I am drafting the 'script' to prepare our presentation to Dr Soon on 25 August. ~ Tyrone=

= Jia Wei: = = Stage 1: I used one of the properties of circles, no matter where the line is, the diameter of the circle will always stay the same. Using this property, I figured that if the base of the triangles must be the diameter of the circle, the bases are the same. The only reason why the area is different is because the height is different. Then I found out that of the base is the same, the tallest height is from an isosceles triangle. =

= Stage 2: I thought that if one of the angles of the isosceles triangle is the same as another triangle, then the length of the line that is opposite the angle that stays the same (as in opposite side in trigonometry) because the angle affects the the other two sides. The other two sides of the triangle must be the same to have the largest area because the perimeter of the triangle may stay the same or even decrease (after one of the sides shifted across the diameter of the circle), which affects the area of the triangle. = = ﻿ Main Question: I found out that the ratio of the height to the base of an equilateral triangle is 866 : 1000 (use sine). Also, (this might help) the area of the largest possible triangle that can be joined in the circle is only a bit more than half of the largest square that can be drawn inside the same circle. The ratio between the area of the square and the circle is 200 : 314 (the area of the square is the circle's diameter multiplied by the radius of the circle that the square is in. So the equilateral triangle's area against the circle's area is a bit more than 100 : 314= = Tyrone: =

=Stage 1:=

=Stage 2:= =Jia Yo﻿﻿ng=

= Stage 1: = = Stage 2: =

=Stage 2:=

=﻿Thanks for all the info. I will be working on many other things too. ~ Tyrone= =﻿= =﻿Please be quick, Jia Wei, the lesson is coming. Thanks ~ Tyrone= =﻿= =Thanks for all the info. Why did you post all the other headings? And if the ratio is 866 : 1000, then we won't have to measure everythig to get the dimensions and area of an equilateral triangle ~ Tyrone=