Following the Pythagorean Theorem and then a bit of deductive addition, we can calculate the relative lengths of the sides of each of the seven tans.
It is worth noting the relationship between the dimensions of the triangle tans, in more detail.
Let the leg length of an isosceles right triangle be x and let the hypotenuse length by y. Using the Pythagorean theorem to solve for the hypotenuse of the triangle,
x + x = y
2x = y
2x = y
2 x = y.
So, the length of the hypotenuse of an isosceles right triangle is 2 times the leg length.
A right isosceles triangle tan has half the area of the right isosceles triangle tan immediately larger than it - the ratio of the areas is 1:2. By similar triangles, we get that the ratio between these two triangles’ side lengths is 1: 2, or the length of one side of a triangle tan is 2 times the same side of the triangle tan immediately smaller than it.
Combining this fact with the one above, we see that the leg length of one triangle tan is the same as the hypotenuse length of the triangle tan immediately smaller than it.
2
2
2
2
2
2
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