Is it possible to have them all irrational?
2006-09-26 06:53:19 · 6 answers · asked by springdaletutor 1 in Science & Mathematics ➔ Mathematics
No. At least one side has to be irrational. The sides have to be in the ratio 1:sqrt(3):2
* * * *
Sorry, didn't notice the second part... sure it is possible for all three to be IRrational. For example, sqrt(2):sqrt(6):2*sqrt(2)
2006-09-26 06:55:39 · answer #1 · answered by Anonymous · 0⤊ 0⤋
If one angle is 30 degrees, the side have to be in the ratio of 1:squre root of 3:2.
But square root of three is not a rational number.
Thus whenever the side shortest side is a rational number the adjecent side will be an irrational number.
2006-09-26 13:58:19 · answer #2 · answered by curious 4 · 1⤊ 0⤋
The RATIOS of the sides of a right angled triangle with one angle 30 will always be OPPOSITE SIDE (of 30 deg) : HYPOTHENUSE : ADJACENT SIDE (of 30 deg)
1 : 2 : square root of 3.
The following possibilities exist: adjacent side irrational and other two sides rational OR adjacent side rational and other two sides irrational.
Not possible for all sides to be rational or all sides to be irrational.
2006-09-26 14:28:45 · answer #3 · answered by Chris G 1 · 0⤊ 0⤋
let's see a right angle is 90 degrees so a right angle triangle with a 30 degree angle would have the following three angles:
90 degrees
30 degrees
60 degrees
Sum of three angles must equal 180 degrees
Just reread and see you are asking dimensions... so...
A squared plus B squared = C squared
not sure of the math tying the ration of lengths B and A to the 30 degree 60 degree split though...
2006-09-26 13:56:05 · answer #4 · answered by Andy FF1,2,CrTr,4,5,6,7,8,9,10 5 · 0⤊ 2⤋
The side opposite the 60 degree angle will be sqrt3 x short side.
If short side is rational, other side is irrational.
Hypotenuse could be 2sqrt5
short side sqrt5
long side sqrt15 all three could be irrational
2006-09-26 14:00:28 · answer #5 · answered by davidosterberg1 6 · 1⤊ 0⤋
Only with a specific kind of triangles: Spherical triangles.
2006-09-26 14:46:11 · answer #6 · answered by · 5 · 0⤊ 0⤋