A 45- 45- 90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?

A 45-45-90 triangle is special. The length's of the two legs will be the same. There's a really easy way to remember it. For this triangle, the ratio of the length of leg:leg:hypotenuse is 1:1:sqrt(2) respectively. So just use the ratio of the length of the hypotenuse to the length of the leg. The same ratio holds for ANY 45-45-90 triangle.

sqrt(2)/1 = 14/x where x is the unknown length of the leg

solving for x:

x = 14/sqrt(2) = 9.899

OR you can just use the pythagoream theorem. keep in mind that the two legs have the same length...

a^2 + b^2 = c^2

but a = b

so 2 a^2 = c^2

a = sqrt( c^2/2 )

a = sqrt( 14^2/2 )

a = 14/sqrt(2)

one leg is 19.80 units, the other is19.80 units and the last one is 28 units The hypotenuse is the unit from the center of the base to the 90 degree angle and bisects that angle creating two 45-45-90 triangles. The hypotenuse is 14 units which constitutes the length of one leg of each of the new triangles. From there it can be deduced that opposite legs on 45 degree angles are equal and the third leg is determined by a^2 + b^2 = C^2. Once C is known then the larger triangle can be solved in the same manner.

I believe there are multiple ways to do this. Draw out your triangle. Label the hypotenuse as c = 14. Label the legs a and b.

First, you can do this using the Pythagorean Theorem.

a^2 + b^2 = c^2

You know that the legs must be equal. It's an isoceles triangle because two angles are equal.

If a = b then...

a^2 + a^2 = c^2

2a^2 = 14^2

2a^2 = 196

a^2 = 98

a = root98 = 7root2

You could also use SOH CAH TOA to solve it. Pick on of the angles. You have the hypotenuse length, and you need either the adjacent or opposite. It doesn't really matter which you use, you will get the same answer.

sin(45) = a/14

14sin(45) = a

Put that into your calculator and you will get the decimal answer of 7root2.

Good luck.

For 45- 45- 90 triangle, the hypotenuse is sqrt(2) times the leg. So the leg equals to hypotenuse/sqrt(2).

14/sqrt(2)

=7sqrt(2)

It's a 45-45-90 triangle, so both of the other legs are equal, so you only need two variables:

x^2+x^2 = c^2

2x^2 = 14^2

2x^2= 196

x^2= 98

x = √(49 *2)

x = 7√2

If x is the length of a leg, then:

x / 14 = sin(45 deg) = sqrt(2) / 2

x = 14 sqrt(2) / 2 = 7sqrt(2).

7 square root 2

let the length of each leg be l, then

2l^2=14^2=196

l^2=98

l=7sqrt(2).

x^2 + x^2 = 14^2

2x^2 = 196

x^2 = 98

x = square root(98) = 9.89949494

divide 14 by the square root of 2 to get your answer.