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The hypotenuse of a 45 degrees -45 degrees -90 degrees triangle measures 10 root of 5 in.

Edited... Answer 5 root of 10

Respuesta :

calculista

Answer:

[tex]5\sqrt{10}\ in[/tex]

Step-by-step explanation:

The question is

Find the measure of the legs

we know that

In a 45 degrees -45 degrees -90 degrees triangle, the measure of the legs are equal

Let

a ----> the measure of one leg

Applying the Pythagorean Theorem

[tex](10\sqrt{5})^2=a^2+a^2[/tex]

solve for a

[tex]500=2a^2[/tex]

Divide by 2 both sides

[tex]a^2=250[/tex]

[tex]a=\sqrt{250}\ in[/tex]

Simplify

[tex]a=5\sqrt{10}\ in[/tex]

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