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Hazel is playing hide-and-seek with Esther and Coral. Esther is hiding 6 meters south of Hazel, and Coral is hiding 8 meters east of Esther. How far apart are Hazel and Coral?

User Rmac
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Answer and Step-by-step explanation:

To determine the distance between Hazel and Coral, we can use the concept of a right-angled triangle formed by the positions of Esther, Hazel, and Coral. Here's how we can calculate the distance:

1. Determine the distance between Hazel and Esther:

Since Esther is hiding 6 meters south of Hazel, the distance between them is 6 meters.

2. Determine the distance between Esther and Coral:

Since Coral is hiding 8 meters east of Esther, the distance between them is 8 meters.

3. Use the Pythagorean theorem to find the distance between Hazel and Coral:

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, Hazel and Coral are the two sides, and we want to find the distance between them, which is the hypotenuse.

So, using the distances we found in steps 1 and 2:

Distance between Hazel and Coral = √(Distance between Hazel and Esther)^2 + (Distance between Esther and Coral)^2

Substituting the values:

Distance between Hazel and Coral = √(6^2 + 8^2)

Distance between Hazel and Coral = √(36 + 64)

Distance between Hazel and Coral = √100

Distance between Hazel and Coral = 10 meters

Therefore, Hazel and Coral are 10 meters apart.

In summary, to find the distance between Hazel and Coral, we used the Pythagorean theorem by finding the distances between Hazel and Esther, and between Esther and Coral. By substituting these values into the theorem, we determined that Hazel and Coral are 10 meters apart.

User Hicham
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