Respuesta :

kudzordzifrancis

Answer:

[tex]|KL|=7\sqrt{2}[/tex]

Step-by-step explanation:

The given triangle is a right triangle.

The m<K=45 degrees.

This means the measure of <L is  also 45 degrees.

This implies that;

|LM|=|KM|=7 units.

From the Pythagoras Theorem;

[tex]|KL|^2=|LM|^2+|KM|^2[/tex]

[tex]|KL|^2=7^2+7^2[/tex]

[tex]|KL|^2=2(7^2)[/tex]

[tex]|KL|=\sqrt{2(7^2)}[/tex]

[tex]|KL|=7\sqrt{2}[/tex]

Option C is correct.

mixter17

Hello!

The answer is:

The third option,

[tex]KL=7\sqrt{2}[/tex]

Why?

Since we are working with a right triangle, we can use the following identity:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

We are given:

[tex]\alpha =45\°\\LM=y=7[/tex]

[tex]hypothenuse=KL[/tex]

Then, substituting and solving we have:

[tex]Sin(45\°)=\frac{7}{hypothenuse}[/tex]

[tex]Hypothenuse=KL=\frac{y}{Sin(45\°)}=\frac{7}{\frac{\sqrt{2} }{2} } \\\\Hypothenuse=KL=7\sqrt{2}[/tex]

Hence, the answer is the third option,

[tex]KL=7\sqrt{2}[/tex]

Have a nice day!

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