Jermaine, Henrietta, And Michael Are Each At Home. Their Relative Locations Are Shown In The Diagram. What Is The Distance Between Michael's House And Henrietta's House? Enter Your Answer In The Box. Round Your Final Answer To The Nearest Mile. Mi 28
Introduction
In this problem, we are tasked with finding the distance between Michael's house and Henrietta's house, given their relative locations as shown in the diagram. To solve this problem, we will employ geometric concepts and techniques to calculate the distance between the two points.
The Diagram: A Visual Representation
Before we dive into the solution, let's take a closer look at the diagram. The diagram shows the relative locations of Jermaine, Henrietta, and Michael's houses. We can see that Jermaine's house is located at a distance of 10 miles from Henrietta's house, and Michael's house is located at a distance of 15 miles from Jermaine's house.
The Pythagorean Theorem: A Fundamental Concept
To find the distance between Michael's house and Henrietta's house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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.
Applying the Pythagorean Theorem
Let's apply the Pythagorean theorem to the triangle formed by Michael's house, Jermaine's house, and Henrietta's house. We can see that the distance between Michael's house and Jermaine's house is 15 miles, and the distance between Jermaine's house and Henrietta's house is 10 miles.
Using the Pythagorean theorem, we can calculate the distance between Michael's house and Henrietta's house as follows:
c² = a² + b²
where c is the distance between Michael's house and Henrietta's house, a is the distance between Michael's house and Jermaine's house (15 miles), and b is the distance between Jermaine's house and Henrietta's house (10 miles).
Plugging in the values, we get:
c² = 15² + 10² c² = 225 + 100 c² = 325
Taking the square root of both sides, we get:
c = √325 c ≈ 18.03 miles
Rounding the Answer
Since we are asked to round our final answer to the nearest mile, we can round 18.03 miles to 18 miles.
Conclusion
In this problem, we used the Pythagorean theorem to calculate the distance between Michael's house and Henrietta's house. By applying the theorem to the triangle formed by the three houses, we were able to find the distance between Michael's house and Henrietta's house as approximately 18 miles.
Key Takeaways
- The Pythagorean theorem is a fundamental concept in geometry that can be used to calculate the distance between two points in a right-angled triangle.
- By applying the Pythagorean theorem to the triangle formed by Michael's house, Jermaine's house, and Henrietta's house, we can calculate the distance between Michael's house and Henrietta's house.
- The distance between Michael's house and Henrietta's house is approximately 18 miles.
Additional Resources
For more information on the Pythagorean theorem and its applications, check out the following resources:
- Khan Academy: Pythagorean Theorem
- Math Is Fun: Pythagorean Theorem
- Wolfram MathWorld: Pythagorean Theorem
Final Answer
Frequently Asked Questions
In this article, we will address some of the most common questions related to the problem of finding the distance between Michael's house and Henrietta's house.
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem is a fundamental concept in geometry that states that in a right-angled 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.
Q: How do I apply the Pythagorean theorem to find the distance between two points?
A: To apply the Pythagorean theorem, you need to identify the two sides of the right-angled triangle and the hypotenuse. Then, you can use the formula c² = a² + b², where c is the length of the hypotenuse, a is the length of one side, and b is the length of the other side.
Q: What if the triangle is not a right-angled triangle? Can I still use the Pythagorean theorem?
A: No, the Pythagorean theorem only applies to right-angled triangles. If the triangle is not a right-angled triangle, you will need to use a different method to find the distance between the two points.
Q: How do I round my answer to the nearest mile?
A: To round your answer to the nearest mile, you need to look at the decimal part of the answer. If the decimal part is less than 0.5, you can round down to the nearest whole number. If the decimal part is 0.5 or greater, you can round up to the nearest whole number.
Q: What if I get a negative answer? Can I still use the Pythagorean theorem?
A: No, the Pythagorean theorem only gives you a positive answer. If you get a negative answer, it means that the triangle is not a right-angled triangle, or that the lengths of the sides are not correct.
Q: Can I use the Pythagorean theorem to find the distance between three points?
A: No, the Pythagorean theorem only applies to two points. If you want to find the distance between three points, you will need to use a different method, such as the law of cosines.
Q: What if I am not sure if the triangle is a right-angled triangle? Can I still use the Pythagorean theorem?
A: No, if you are not sure if the triangle is a right-angled triangle, you should not use the Pythagorean theorem. Instead, you should use a different method to find the distance between the two points.
Conclusion
In this article, we have addressed some of the most common questions related to the problem of finding the distance between Michael's house and Henrietta's house. We have also provided some additional resources for further learning.
Additional Resources
For more information on the Pythagorean theorem and its applications, check out the following resources:
- Khan Academy: Pythagorean Theorem
- Math Is Fun: Pythagorean Theorem
- Wolfram MathWorld: Pythagorean Theorem
Final Answer
The final answer is: 18