Question 8 of 25

In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg?

A. [tex]$1: \sqrt{2}$[/tex]

B. [tex][tex]$1: 1$[/tex][/tex]

C. [tex]$2: 1$[/tex]

D. [tex]$\sqrt{2}: 1$[/tex]



Answer :

To determine the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle, we need to understand the properties of this specific type of right triangle.

A 45-45-90 triangle is a special kind of right triangle where the two non-hypotenuse sides (legs) are of equal length because the angles opposite these sides are equal (both 45 degrees).

Here’s a step-by-step explanation:

1. Identify the properties of a 45-45-90 triangle:
- The two angles adjacent to the right angle are both 45 degrees.
- The two legs of the triangle are of equal length.

2. Set up the ratio:
- Let each leg of the triangle be of length [tex]\( L \)[/tex].
- Since both legs are of equal length, the ratio of one leg to the other is [tex]\( \frac{L}{L} \)[/tex].

3. Simplify the ratio:
- [tex]\( \frac{L}{L} = 1 \)[/tex]

Therefore, the ratio of the length of one leg to the length of the other leg in a 45-45-90 triangle is [tex]\( 1:1 \)[/tex].

So, the correct answer is [tex]\( B \)[/tex].