Geometry, ch. 3: Pythagorean triples vs. 30-60-90 'rule'

[frederikkem]

Hey,

I ran into a problem with the 'check your skills' question 9 in chapter 4, where you have to find the missing side of a triangle to calculate the perimeter and area of a rectangle.

I tried to apply the rule for the ratio of the lengths of a 30-60-90 triangle (as found on page 58), but it was pretty clear that with a short side of 6, and a hypotenuse of 10, it didn't really fit that ratio, because then the hypotenuse should have been 12. From the solution I then find out that this is a pythagorean triple (as shown on page 54).

So my question is, when does the 30-60-90 rule apply? Only for non-pythagorean 30-60-90 triangles? Or something else? The way the rule of the ratio of the lengths is written in the book, I thought it applied to ALL 30-60-90 triangles. What is it that I have missed?

Thanks in advance!

[tommywallach]

It does apply to all 30-60-90 triangles. Nothing in this figure tells you any of the angles, so I'm not sure why you thought it was 30-60-90...

-t