Respuesta :

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]

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