Final answer:
To find the distance between Emma and her younger sister, we use the Pythagorean theorem on the right triangle formed by Emma, her brother, and her sister. The distance is calculated to be the square root of 39, which is approximately 6.2 feet when rounded to the nearest tenth.
Step-by-step explanation:
Understanding the Distance in a Triangle Formation
Emma is in an assembly, and based on her observations, we are dealing with a right triangle situation. Emma's younger sister is to her right, and her older brother is 5 feet ahead of her. The distance directly between Emma's brother and her sister is 8 feet. To find the distance between Emma and her younger sister, we need to calculate the third side of the triangle, which will be the horizontal leg adjacent to Emma.
Using the Pythagorean theorem which states that in a right-angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²), we can find the required distance:
Substituting into Pythagorean theorem: x² + 5² = 8².
So, x² = 64 - 25 = 39.
Therefore, x = √39 ≈ 6.2 feet.
The answer, rounded to the nearest tenth, is that Emma and her younger sister are approximately 6.2 feet apart.