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
Introduction
In this article, we will explore the concept of calculating distances between two points, using a real-world scenario as an example. We will apply mathematical principles to determine the distance between Michael's house and Henrietta's house, based on their relative locations shown in the diagram.
Understanding the Diagram
The diagram shows the relative locations of Jermaine, Henrietta, and Michael's houses. To calculate the distance between Michael's house and Henrietta's house, we need to understand the layout of the diagram. The diagram shows that Jermaine's house is located 3 miles east of Michael's house, and Henrietta's house is located 4 miles north of Jermaine's house.
Calculating the Distance
To calculate 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.
The Pythagorean Theorem
The Pythagorean theorem can be expressed mathematically as:
a^2 + b^2 = c^2
where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse.
Applying the Pythagorean Theorem
In this case, we can let a = 3 miles (the distance between Michael's house and Jermaine's house) and b = 4 miles (the distance between Jermaine's house and Henrietta's house). We want to find the distance between Michael's house and Henrietta's house, which is the length of the hypotenuse, c.
Plugging in the Values
Substituting the values into the Pythagorean theorem, we get:
3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2
Solving for c
To find the value of c, we take the square root of both sides of the equation:
c = √25 c = 5
Conclusion
Therefore, the distance between Michael's house and Henrietta's house is 5 miles.
Rounding the Answer
Since we are asked to round our final answer to the nearest mile, we can round 5 miles to 5 miles.
Final Answer
The final answer is: 5 miles
Additional Information
It's worth noting that the Pythagorean theorem can be used to calculate distances in a variety of situations, not just in the context of right-angled triangles. Additionally, the theorem can be used to calculate the length of the hypotenuse in a right-angled triangle, given the lengths of the other two sides.
Real-World Applications
The Pythagorean theorem has numerous real-world applications, including:
- Calculating distances between two points on a map
- Determining the length of a diagonal in a rectangle or square
- Calculating the height of a building or a mountain
- Determining the distance between two points on a coordinate plane
Conclusion
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem is a mathematical formula that describes the relationship between the lengths of the sides of a right-angled triangle. It states that 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 use the Pythagorean theorem to calculate distances?
A: To use the Pythagorean theorem to calculate distances, you need to know the lengths of the two sides that form the right angle and the length of the hypotenuse. You can then plug these values into the formula:
a^2 + b^2 = c^2
where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse.
Q: What if I don't know the length of the hypotenuse?
A: If you don't know the length of the hypotenuse, you can use the Pythagorean theorem to calculate it. Simply plug in the values of the other two sides into the formula, and solve for c.
Q: Can I use the Pythagorean theorem to calculate distances in non-right-angled triangles?
A: No, the Pythagorean theorem only works for right-angled triangles. If you have a non-right-angled triangle, you will need to use a different method to calculate the distance between two points.
Q: What are some real-world applications of the Pythagorean theorem?
A: The Pythagorean theorem has numerous real-world applications, including:
- Calculating distances between two points on a map
- Determining the length of a diagonal in a rectangle or square
- Calculating the height of a building or a mountain
- Determining the distance between two points on a coordinate plane
Q: Can I use the Pythagorean theorem to calculate distances in three dimensions?
A: Yes, the Pythagorean theorem can be extended to three dimensions. In this case, you will need to use the formula:
a^2 + b^2 + c^2 = d^2
where a, b, and c are the lengths of the three sides that form the right angle, and d is the length of the hypotenuse.
Q: What if I make a mistake when using the Pythagorean theorem?
A: If you make a mistake when using the Pythagorean theorem, you may end up with an incorrect answer. To avoid this, make sure to double-check your calculations and use a calculator or other tool to help you with the math.
Q: Can I use the Pythagorean theorem to calculate distances in different units?
A: Yes, the Pythagorean theorem can be used to calculate distances in different units, such as miles, kilometers, or feet. Simply make sure to use the correct units when plugging in the values into the formula.
Q: Is the Pythagorean theorem only used in mathematics?
A: No, the Pythagorean theorem has applications in many fields, including physics, engineering, and computer science. It is a fundamental concept in mathematics, but it has many real-world applications as well.
Conclusion
In conclusion, the Pythagorean theorem is a powerful mathematical tool that can be used to calculate distances between two points. By understanding how to use the theorem, you can apply it to a wide range of real-world situations. Whether you are working with geometry, trigonometry, or other mathematical concepts, the Pythagorean theorem is an essential tool to have in your toolkit.