45 45 90 triangles??

Question

how do u find the lengths? i know u use the pythagorean theorem but can u walk me through it?

ex: the two equal sides are unknown and the other side is 12.

thank you!

Answer 1

You don't necessarily need to know the Pythagorean Theorem for this. The legs of a 45-45-90 triangle are always the length of x and the hypotenuse of the triangle is x*sqrt(2). So solve for x:

x*sqrt2 = 12

x = 12/sqrt(2)

x = 12sqrt(2) / 2

x = 6sqrt(2)

And that's the length of the two legs. You could find it using the Pythagorean Theorem, but knowing the ratios of the sides is easier.

Answer 2

Lets call the side that are equal x.

Then the pythagorian theorem states that a^2+b^2=c^2

So in this case c=12 and a and b equal x.

Now the new equation is:

x^2+x^2=144

2x^2=144

x^2=72

x=sqrt(72)

Hope this helps!

Answer 3

The hypotenuse (longest side) is the square root of two (otherwise known as radical 2) multiplied by the shortest side.

So if the hypotenuse is 12,

then the legs would be 12 / radical 2

Then you simplify that cuz a radical can't be in the denominator, so multiply both numerator and denominator by rad2, so you get 12 rad 2 over 2, which simplifies to 6 rad 2.

Check, 6 rad 2 x rad 2 = 6 x 2= 12.

YAY!

Answer 4

a=b

c=12

a^2+b^2=c^2