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].
