45-45-90 degree triangle?

Question

A 45-45-90 triangle has a hypotenuse of length 7. What is the length of one of its legs? If necessary, round your answer to two decimal places.

argh. anyone know?

Answer 1

a^2 + b^2 = c^2
a = b (its a regular right triangle)
a^2 + a^2 = c^2
2a^2 = 7^2
2a^2 = 49
a^2 = 24.5
a = the square root of 24.5
a = 4.9497
rounded to two places, 4.95
=)

Answer 2

Each leg is 7(sqrt(2))/2.

There is a law of triangles that the length of the hypotenuse of a right triangle with congruent angles (your 45-45-90) is the length of one of the legs times the square root of 2.

So, the leg is 7 divided by the square root of 2. This is 4.95.

Why is the length of the hypotenuse always the square root of 2 times the length of the leg in a 45-45-90 triangle? Recall the ubiquitous:
a^2 + b^2 = c^2

Since a = b, you have:
a^2 + a^2 = c^2
2a^2 = c^2
sqrt(2) * a = c

Answer 3

let the 2 represent a squared function here so you can understand.. a2+b2=c2 a and b are the same, c2=144 144 divided by 2 =72 the length of the side would be radical72, but it needs to be simplified to it would be 3radical8 but there is another way to solve it, a 45 45 90 triangle as a ratio, the two sides are 1, and the hypotenuse is radical2, so you can make a proportion putting 1/x = radical2/12 and then cross multiply and you would get 6radical2, which = radical72

Answer 4

It is isosceles. Let x represent the length of one of the equal legs.

x^2 + x^2 = 7^2 using Pythagorean Theorem since it is a right triangle as well

2x^2 = 49
x^2 = 49/2
x^2 = 24.5
x = sqrt of 24.5
x = 4.95 approx

Answer 5

You have an orthogonal 45-degree triangle and therefore, you can use the Pythagorean theorem to find the length of each of the other two sides, which should be of the same length.

Try this URL to learn a few things.

http://mathforum.org/dr.math/faq/faq.pyt...

Answer 6

Answer=5.0

Here's how it's figured by Pythagoreum Theorum:
a^2 + b^2 = c^2 where c is the hypotenuse of length 7.
In this case, side a= side b, so by substitution:
2 * a^2 = c^2
Solving for hypotenuse a gives:
a = c/(sqrt 2) = c/1.414
Substituting c=7
a = 7/1.414
a = 5.0

Answer 7

Pythagorean Theorem!!!!!!
You SHOULD know that if two angles are equal then so are the opposing sides! (try to draw it otherwise!) so the P.T. gives 7*7 = x*x+x*x do the math (where x is the length of a side)

Answer 8

Well, they're both the same length, and Pythagoras' theorem says that length is 7/ sqr 2, which is 4.95.

Answer 9

Sin 45 = opp/hypo

Sin 45 = opp/ 7

therefore, opp = 7x Sin 45

Answer 10

a^2 + b^2 = c^2. a = b. Therefore a^2 + a^2 = c^2
2a^2 = c^2 = 7^2 = 49
2a^2 = 49, a^2 = 24.5, a = sq. rt. of 24.5 = 4.95