Certainly! Let's solve this step-by-step.
Step 1: Understand the properties of a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle.
- This is a special type of isosceles right triangle where the two legs are of equal length.
- The ratio of the lengths of the legs to the hypotenuse in a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle is [tex]\(1:1:\sqrt{2}\)[/tex].
Step 2: Given data.
- The hypotenuse measures [tex]\(24\)[/tex] inches.
Step 3: Use the ratio properties to determine the length of one leg.
- Since we know the hypotenuse is [tex]\(24\)[/tex] inches and the ratio of the legs to the hypotenuse is [tex]\(1:\sqrt{2}\)[/tex], we know that each leg of the triangle is [tex]\(\frac{\text{hypotenuse}}{\sqrt{2}}\)[/tex].
Step 4: Calculate the length of one leg.
- Therefore, the length of one leg is [tex]\(\frac{24}{\sqrt{2}}\)[/tex].
Step 5: Simplify the result.
- Simplifying [tex]\(\frac{24}{\sqrt{2}}\)[/tex] gives us approximately [tex]\(16.97056274847714\)[/tex] inches.
So, the length of one of the legs of the [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle is [tex]\(16.97056274847714\)[/tex] inches. The nearest correct option is not provided in the choices listed, but this is the accurate result.
