Final answer:
Melissa and her younger sister are 5 meters apart.
Step-by-step explanation:
In this scenario, Melissa's younger sister is directly to her right and her older brother is 12 meters directly ahead of her. Since her brother and sister are 13 meters apart, we can use the Pythagorean theorem to find the distance between Melissa and her younger sister.
Let's call the distance between Melissa and her younger sister 'x'. We can set up a right triangle with Melissa, her brother, and her sister as the vertices.
Using the Pythagorean theorem, we have:
x^2 + 12^2 = 13^2
Simplifying the equation, we get:
x^2 + 144 = 169
x^2 = 169 - 144
x^2 = 25
Taking the square root of both sides, we find:
x = 5
Therefore, Melissa and her younger sister are 5 meters apart.