Forgot this about Geometry..?

Question

If you split a rectangle in half by its diagonals, do the resulting ratios for the triangles side lengths become a 30-60-90 triangle? (2:sqrt(3):1)

Answer 1

well it depends on the dimensions of the rectangle...

if it is a 1 by 1 (ie a square) the angles are 90 and 45 and 45
and the other side is SQRT{2}

if it is a 2 by 1 rectangle the sides are 1, 2 and SQRT{5}
as 1^2 + 2^2 = 5

however if the rectangle was a 1 by SQRT{3} rectangle (or sides of same ratio)
the new sides are 1 , SQRT 3 and 2
and the angles are 30 60 and 90 as above....

so it all depends on the original rectangle really.. use trig and pythagoras to work it out

Answer 2

Not necessarily. It depends on the ratios of the sides.

Like a 1:2 rectangle will have different angles for the bisected triangles then a 1:3 or a 1:4 will

It depends on the right triangle trigonometry. Actually, i think a 1:2 rectangle WILL give a 30,60,90 triangle. But once again, it depends on the right triangle trigonometry.

Answer 3

No. This would be true only in the special case where the diagonal is twice the rectangle's width.