how do i find the length of each leg in a 45-45-90 triangle?

Question

here is the link to the kind of triangles im talking about... how would i go about solving this?

http://i131.photobucket.com/albums/p285/pickapet1/6523d5be-e8ba-44a3-9eb4-560b06940cd.gif

A. square root of 32
B. 4 square root of 2
C. 16 square root of 2
D. 5.6
E. 16
F. 1

Answer 1

Two legs are equal; the third (hypotenuse) is longer than the others by a factor of square root of 2. (Pythagoras.)

Answer 2

God I can't remember...

Well I know that the two legs (the segments between 90 and 40 degrees) can be squared and added together, and then divided by two, which has to equal the longest leg, 32 units.

So the famous mathematical formula (a.k.a. Pythagorean Theory) states that a^2 + b^2 = c^2.

Here's what we have so far, based on the given information.
a^2 + b^2 = 32 units

So 32 squared = 1024
1024 must equal a^2 + b^2
1024 = a^2 + b^2
1024 = 512 + 512
1024 = v/512 + v/512
1024 = 22.6274717^2 + 22.6274717^2
Length of the two legs are 22.6274717 units long
Length of the long leg is 32 units long

There ya go.

Answer 3

The Pythagorian Theorem is that A squared + B squared = C squared. C would be your hypotenuse. So take the square of 32 (which is 1024), divide it by 2, and you get 512. You can do this because A and B are the exact same length in this problem. Now find the square root of 512... (which is around 22.6) and you have your answer.

Answer 4

To put it easily, 2(X^2)=32^2

X^2=512/2

X^2=512

X= SQRT512

X=22.63

Answer 5

the legs (rays that make up the right angle) are equal. the hypotonuse (line opposite of the legs) equals leg1*leg1 + leg2*leg2.