45-45-90 degree triangle question?

Question

A 45-45-90 triangle has a hypotenuse of length 12. What is the length of one of the legs? If necessary, round your answer to two decimal places.

anyone know?

Answer 1

let the side opposite to angle 45 be L
by using Pythagoras's theorem
L^2+L^2=12^2
2L^2=144 /2
L^2=72
L=sq. root of 72=8.49

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

for a 45-45-90 triangle, the legs are h√2 /2=12√2 /2
or 6√2=8.49

Answer 5

I'm guessing this is homework, so I won't give you the answer, but I'll get you started:

for a right triangle (which this is, because it has a 90* angle), use the Pythagorean theorem, which says:

a^2 + b^2 = c^2

where a & b are legs and c is the hypoteneuse.

since the non-right angles have the same measurement (45*), the legs are the same length, so a = b

it should be easy algebra from there.

Answer 6

By Pythagora's theorem we have : a^2 + b^2 = c^2

If angle A = angle b = 45 degrés then side a = side b

c = hypothenuse = 12

right angle = 90 degres


So a^2 + b^2 = c^2

a^2 + a^2 = c^2

2a^2 = c^2

c = sqrt 2 a^2

= sqrt 2 x a

12 = a sqrt 2

a = 12/sqrt 2

= 12/ 1.4142

= 8,49

Answer = 8,49

Answer 7

A 45-45-90 triangle has sides n:n:n*sqrt(2) for some positive real n.
So the answer is 12/sqrt(2) or 6sqrt(2).

Answer 8

9

Answer 9

It's a right triangle, the equation used is a^2 + b^2 = c^2.

However we know that c = 12, and a = b, since the extra angles are both 45.

2a^2 = 12^2
2a^2 = 144
a^2 = 72
a = sqrt(72) = 8.48 or 6rad2

Answer 10

The 45-90-45 triangle is in fact half of a square. The relation of a diagonal of a square is a*sqrt2, for a side equal a. So we have an equation:
12=a*sqrt2 /sqrt2 |we divide by sqrt2 to get a
12/sqrt2=a | sqrt2 equals more or less 1, 41, so we'll put that there.
a=12 / 1.41 = 8.5106383 |result (using google calculator)
a=8.51 |Your answer :)