Question

Leave your answer in simplest radical form

Answer 1

Hello!

The answer is:

The third option,

$KL=7\sqrt{2}$

Why?

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

$Sin(\alpha)=\frac{y}{hypothenuse}$

We are given:

$\alpha =45\°\\LM=y=7$

$hypothenuse=KL$

Then, substituting and solving we have:

$Sin(45\°)=\frac{7}{hypothenuse}$

$Hypothenuse=KL=\frac{y}{Sin(45\°)}=\frac{7}{\frac{\sqrt{2} }{2} } \\\\Hypothenuse=KL=7\sqrt{2}$

Hence, the answer is the third option,

$KL=7\sqrt{2}$

Have a nice day!

Answer 2

Answer:

$|KL|=7\sqrt{2}$

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;

$|KL|^2=|LM|^2+|KM|^2$

$|KL|^2=7^2+7^2$

$|KL|^2=2(7^2)$

$|KL|=\sqrt{2(7^2)}$

$|KL|=7\sqrt{2}$

Option C is correct.