Question

The hypotenuse of a 45 45 90 triangle measures 24 inches. what is the length of one leg of the triangle?

Answer 1

Answer:

Step-by-step explanation:

Given that in a right triangle, angles are 45 45 90

A 45 – 45 – 90 degree triangle (or isosceles right triangle) is a triangle with angles of 45°, 45°, and 90° and sides in the ratio of. Note that it's the shape of half a square, cut along the square's diagonal, and that it's also an isosceles triangle (both legs have the same length).

The hypotenuse measures 24 inches.

Since the other two angles are equal, we find that two legs would be equal

Let each leg = x

Then apply Pythagorean theorem to get $x^2+x^2 = 24^2\\x=12\sqrt{2}$

Thus we get

each leg of the right triangle = 12√2

Answer 2

Answer:

$12\sqrt{2}\ in$

Step-by-step explanation:

we know that

A $45\°-45\°-90\°$ right triangle has two equal legs

Let

x-----> the length side of the leg of the triangle

y------> the length side of the hypotenuse

$sin(45\°)=cos(45\°)=\frac{\sqrt{2}}{2}$

$cos(45\°)=\frac{x}{y}$

so

$\frac{x}{y}=\frac{\sqrt{2}}{2}$

in this problem we have

$y=24\ in$

substitute the value of y and solve for x

$\frac{x}{24}=\frac{\sqrt{2}}{2}$

$x=24\frac{\sqrt{2}}{2}$

$x=12\sqrt{2}\ in$