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ANSWER

The correct answer is A.

EXPLANATION

The given triangle is a right isosceles triangle because one angle is 90° and the base angles will be 45° each.

This means that:

[tex]a = b[/tex]

Using, the Pythagorean Theorem, we have

[tex] {a}^{2} + {a}^{2} = {(9 \sqrt{2} )}^{2} [/tex]

We simplify to get:

[tex]2{a}^{2} = 81 \times 2[/tex]

[tex]{a}^{2} = 81[/tex]

Take positive square root,

[tex]a = \sqrt{81} [/tex]

This implies that

[tex]a = 9[/tex]

Therefore b is also equal to 9

The correct answer is A.

luisejr77

Answer: option a

Step-by-step explanation:

You can use these identities:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

Then, to find "a" you know that:

[tex]\alpha=45\°\\adjacent=a\\hypotenuse=9\sqrt{2}[/tex]

Substituting:

[tex]cos(45\°)=\frac{a}{9\sqrt{2}}[/tex]

Now you must solve for "a":

[tex]a=cos(45\°)(9\sqrt{2})\\\\a=9in[/tex]

To find  "b", you know that:

[tex]\alpha=45\°\\opposite=b\\hypotenuse=9\sqrt{2}[/tex]

Substituting:

[tex]sin(45\°)=\frac{b}{9\sqrt{2}}[/tex]

Now you must solve for "b":

[tex]b=sin(45\°)(9\sqrt{2})\\\\b=9in[/tex]

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