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Abby looks around at an assembly. She notices her younger sister to her right and her older brother $15$ meters ahead of her. If Abby's brother and sister are $17$ meters apart, how far apart are Abby and her younger sister?_____meters

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Pythagorean theorem: word problems

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Q. Abby looks around at an assembly. She notices her younger sister to her right and her older brother

15

meters ahead of her. If Abby's brother and sister are

17

meters apart, how far apart are Abby and her younger sister?_____meters

Identify Triangle Formed: Identify the triangle formed by Abby, her brother, and her sister. Abby's brother is $15$ meters ahead, forming one leg of the triangle. The distance between the brother and the sister is $17$ meters, forming the hypotenuse. We need to find the distance between Abby and her sister, which is the other leg of the triangle.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem. Let $x$ be the distance between Abby and her sister. Then, according to the theorem: $\newline$ $15^2 + x^2 = 17^2$ $\newline$ $225 + x^2 = 289$
Solve for x^ $2$ : Solve for $x^2$ : $\newline$ $x^2 = 289 - 225$ $\newline$ $x^2 = 64$
Find x: Find $x$ by taking the square root of $x^2$ : $\newline$ $x = \sqrt{64}$ $\newline$ $x = 8$ meters.

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