The required length of a leg of a right triangle is [tex]10\sqrt{2}[/tex].
Given that,
Apply the 45º-45º-90º Triangle Theorem.
The length of the hypotenuse is 10 in.
We have to determine,
The length of a leg of a right triangle.
According to the question,
A 45°-45°-90° triangle is a special right triangle that has two 45-degree angles and one 90-degree angle. The side lengths of this triangle are in the ratio;
Hypotenuse = n: n: n√2
The 45°-45°-90° right triangle is half of a square. This is because the square has each angle equal to 90°, and when it is cut diagonally, the one angle remains as 90°, and the other two 90° angles bisected (cut into half) and become 45° each.
The diagonal of a square becomes the hypotenuse of a right triangle, and the other two sides of a square become the two sides (base and opposite) of a right triangle.
Then,
Side 1: Side 2: Hypotenuse = n: n: n√2
[tex]=n \times \sqrt{2}\\\\=10 \sqrt{2}[/tex]
Hence, The required length of a leg of a right triangle is [tex]10\sqrt{2}[/tex].
To know more about Triangles click the given below.
https://brainly.com/question/4378063
