Sure, let's solve the problem step by step.
A 45-45-90 triangle is a special type of right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. Since two of the angles are 45 degrees, this means the triangle is isosceles, and thus the two legs of the triangle are of equal length.
Here is a step-by-step solution:
1. Identify the properties of a 45-45-90 triangle:
- The legs of the triangle are equal in length because it is an isosceles right triangle.
- The hypotenuse is [tex]\(\sqrt{2}\)[/tex] times longer than each leg.
2. Determine the relationship between the legs:
- Let’s denote the length of one leg as [tex]\(a\)[/tex]. Because the legs are equal, the other leg will also have the length [tex]\(a\)[/tex].
3. Calculate the ratio of the lengths of the legs:
- Since both legs are equal, the ratio of the length of one leg to the other is simply
[tex]\[
\text{Ratio} = \frac{a}{a} = 1
\][/tex]
Therefore, the correct answer is:
C. [tex]\(1:1\)[/tex]
The ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is [tex]\(1:1\)[/tex].
