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Three ballet dancers are positioned on stage. If Rita is $8\,\text{meters}$ straight behind Ava and $6\,\text{meters}$ directly left of Meg, how far is Ava from Meg? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

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Q. Three ballet dancers are positioned on stage. If Rita is

8\,\text{meters}

straight behind Ava and

6\,\text{meters}

directly left of Meg, how far is Ava from Meg?

\newline

\_\_\_\_\_

meters

Form Right Triangle: Rita is $8$ meters behind Ava and $6$ meters left of Meg, so we can form a right triangle with Rita at the right angle, Ava and Meg at the other two points.
Calculate Distance Rita-Ava: The distance between Rita and Ava is one leg of the triangle, which is $8$ meters.
Calculate Distance Rita-Meg: The distance between Rita and Meg is the other leg of the triangle, which is $6$ meters.
Use Pythagorean Theorem: To find the distance between Ava and Meg, we use the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse (the distance between Ava and Meg).
Plug in Values: Plug in the values: $8^2 + 6^2 = c^2$ .
Calculate Squares: Calculate the squares: $64 + 36 = c^2$ .
Add Squares: Add the squares: $64 + 36 = 100$ .
Find Value of c: Find the value of $c$ : $c^2 = 100$ .
Take Square Root: Take the square root of both sides: $c = \sqrt{100}$ .
Calculate Square Root: Calculate the square root: $c = \sqrt{10}$ .

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