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Three ballet dancers are positioned on stage. Kate is straight behind Maura and directly left of Craig. If Maura and Kate are $7$ meters apart, and Craig and Maura are $9$ meters apart, what is the distance between Kate and Craig? If necessary, round to the nearest tenth. $\newline$ meters

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Pythagorean theorem

Full solution

Q. Three ballet dancers are positioned on stage. Kate is straight behind Maura and directly left of Craig. If Maura and Kate are

7

meters apart, and Craig and Maura are

9

meters apart, what is the distance between Kate and Craig? If necessary, round to the nearest tenth.

\newline

meters

Identify Positions and Distances: Identify the positions of the ballet dancers and the distances between them. $\newline$ Kate is directly behind Maura, and Craig is directly to the left of Maura. This forms a right-angled triangle with Kate, Maura, and Craig at the vertices. $\newline$ Distance between Maura and Kate: $7$ meters (this is one leg of the triangle). $\newline$ Distance between Craig and Maura: $9$ meters (this is the other leg of the triangle). $\newline$ The distance between Kate and Craig is the hypotenuse of the right-angled triangle.
Form Right-Angled Triangle: Apply the Pythagorean Theorem to find the distance between Kate and Craig. $\newline$ The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ . $\newline$ Let's denote the distance between Kate and Craig as $c$ . $\newline$ We have: $a = 7$ meters, $b = 9$ meters, and we need to find $c$ . $\newline$ The equation is: $a^2 + b^2 = c^2$ .
Apply Pythagorean Theorem: Plug in the known values and calculate $c$ . $7^2 + 9^2 = c^2$ $49 + 81 = c^2$ $130 = c^2$
Calculate Distance: Solve for $c$ by taking the square root of both sides of the equation. $c = \sqrt{130}$ $c \approx 11.4$ meters (rounded to the nearest tenth)

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