To find the length of one of the legs of a 45-45-90 triangle when the hypotenuse is given, we can use the properties of this specific type of triangle. In a 45-45-90 triangle, the legs are congruent, which means they have the same length. There is a specific relationship between the lengths of the legs and the hypotenuse: the length of each leg is equal to the length of the hypotenuse divided by the square root of 2.
Let's follow the steps to find the length of one leg:
1. Given:
[tex]\[
\text{Hypotenuse} = 10 \text{ units}
\][/tex]
2. Formula:
In a 45-45-90 triangle, each leg [tex]\( L \)[/tex] is given by:
[tex]\[
L = \frac{\text{Hypotenuse}}{\sqrt{2}}
\][/tex]
3. Substitute the given hypotenuse into the formula:
[tex]\[
L = \frac{10}{\sqrt{2}}
\][/tex]
4. Simplify the expression:
To make the division simpler:
[tex]\[
L = \frac{10}{\sqrt{2}} \approx 7.071067811865475 \text{ units}
\][/tex]
Thus, the length of each leg of the 45-45-90 triangle is approximately [tex]\( 7.071067811865475 \)[/tex] units. Given the options:
A. [tex]\( 5 \sqrt{2} \)[/tex] units
B. 5 units
C. 10 units
D. [tex]\( 10 \sqrt{2} \)[/tex] units
The correct answer is the value closest to [tex]\( 7.071067811865475 \)[/tex] units, but none of the provided options exactly match this numerical value. This suggests checking again or the provided options may not be based on exact simplification techniques shown above. In the given scenario, conversion to exact decimal can help if the value is approximated.
