# Thread: 30 60 90 right triangles

1. ## 30 60 90 right triangles

ok if you said the side opposite 30 is x, the hyp. is 2x, and the other side is root 3, would that be correct?

i tutored someone in geometry and the book said the hyp. is x and the other sides are root 3/2 and 1/2x but i multiplied all the numbers by 2 when i showed it to her because i thought it seemed simpler and easier to remember ....uhmmm since it's the same ratio between the sides isn't it the same????

2. Originally Posted by desperate_on_sunday_night
ok if you said the side opposite 30 is x, the hyp. is 2x, and the other side is root 3, would that be correct?
Yes its correct

Why
Pythagoras Theorem

$\displaystyle Hypotnuse^2 = Base^2 + Altitude^2$

$\displaystyle (2x)^2 = x^2 + (\sqrt{3})^2$

$\displaystyle 3x^2 = 3$

$\displaystyle x^2 =1$

$\displaystyle x = \pm 1$

We need length which is always positive
Hence x= 1

Thus this is a right triangle with base = 1 altitude= squareroot(3) & hypotnuse =2

3. Originally Posted by desperate_on_sunday_night
ok if you said the side opposite 30 is x, the hyp. is 2x, and the other side is root 3, would that be correct?

i tutored someone in geometry and the book said the hyp. is x and the other sides are root 3/2 and 1/2x but i multiplied all the numbers by 2 when i showed it to her because i thought it seemed simpler and easier to remember ....uhmmm since it's the same ratio between the sides isn't it the same????
Well, the third side is $\displaystyle \sqrt{3} x$. Is that what you meant?