Answer:
The lenghts of both legs: [tex]\frac{15\sqrt{2}}{2}\ inches[/tex]
Step-by-step explanation:
By definition, when a triangle has angles that measures 45°, 45° and 90°, its legs are congruent.
Then, knowing the lenght of the hypotenuse, we can find the lenght (in inches) of any leg of the given triangle by applying the Trigonometric Identity [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:
[tex]sin(45\°)=\frac{leg}{15}\\\\leg=\frac{15}{\sqrt{2}}[/tex]
Finally, simplifying, we get:
[tex]leg=\frac{15(\sqrt{2})}{(\sqrt{2})(\sqrt{2})}=\frac{15\sqrt{2}}{2}[/tex]