Evaluate The Formula For \[$ C \$\]:$\[ C = \sqrt{a^2 + B^2} \\]Given:- \[$ A = 8 \$\]- \[$ B = 15 \$\]
Introduction
In mathematics, the formula for calculating the distance between two points in a coordinate plane is a fundamental concept. The formula, denoted as c, is given by the equation c = √(a^2 + b^2), where a and b are the coordinates of the two points. In this article, we will evaluate the formula for distance using the given values of a = 8 and b = 15.
Understanding the Formula
The formula for distance is based on the Pythagorean theorem, which 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. In the context of the formula for distance, the two sides are represented by the coordinates a and b, and the hypotenuse is represented by the distance c.
Calculating the Distance
To calculate the distance c, we need to substitute the given values of a and b into the formula. In this case, a = 8 and b = 15. Plugging these values into the formula, we get:
c = √(8^2 + 15^2)
Simplifying the Equation
To simplify the equation, we need to calculate the squares of a and b. The square of a is 8^2 = 64, and the square of b is 15^2 = 225. Substituting these values into the equation, we get:
c = √(64 + 225)
Evaluating the Sum
The next step is to evaluate the sum inside the square root. Adding 64 and 225, we get:
c = √289
Calculating the Square Root
The final step is to calculate the square root of 289. The square root of 289 is 17.
Conclusion
In conclusion, we have evaluated the formula for distance using the given values of a = 8 and b = 15. By substituting these values into the formula, simplifying the equation, and calculating the square root, we found that the distance c is equal to 17.
Real-World Applications
The formula for distance has numerous real-world applications, including:
- Navigation: The formula is used in navigation systems to calculate the distance between two points on a map.
- Surveying: The formula is used in surveying to calculate the distance between two points on a property.
- Physics: The formula is used in physics to calculate the distance traveled by an object under the influence of a constant acceleration.
Common Mistakes
When evaluating the formula for distance, there are several common mistakes to avoid:
- Incorrect calculation of the squares: Make sure to calculate the squares of a and b correctly.
- Incorrect evaluation of the sum: Make sure to evaluate the sum inside the square root correctly.
- Incorrect calculation of the square root: Make sure to calculate the square root correctly.
Tips and Tricks
Here are some tips and tricks to help you evaluate the formula for distance:
- Use a calculator: Use a calculator to simplify the equation and calculate the square root.
- Check your work: Double-check your work to ensure that you have calculated the squares, evaluated the sum, and calculated the square root correctly.
- Practice, practice, practice: Practice evaluating the formula for distance with different values of a and b to become more comfortable with the calculation.
Conclusion
Introduction
In our previous article, we evaluated the formula for distance using the given values of a = 8 and b = 15. In this article, we will answer some frequently asked questions about the formula for distance.
Q: What is the formula for distance?
A: The formula for distance is c = √(a^2 + b^2), where a and b are the coordinates of the two points.
Q: What is the significance of the Pythagorean theorem in the formula for distance?
A: The Pythagorean theorem is a fundamental concept in mathematics 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. In the context of the formula for distance, the two sides are represented by the coordinates a and b, and the hypotenuse is represented by the distance c.
Q: How do I calculate the distance between two points in a coordinate plane?
A: To calculate the distance between two points in a coordinate plane, you need to substitute the given values of a and b into the formula c = √(a^2 + b^2). Then, simplify the equation by calculating the squares of a and b, evaluating the sum inside the square root, and calculating the square root.
Q: What are some common mistakes to avoid when evaluating the formula for distance?
A: Some common mistakes to avoid when evaluating the formula for distance include:
- Incorrect calculation of the squares: Make sure to calculate the squares of a and b correctly.
- Incorrect evaluation of the sum: Make sure to evaluate the sum inside the square root correctly.
- Incorrect calculation of the square root: Make sure to calculate the square root correctly.
Q: How do I use the formula for distance in real-world applications?
A: The formula for distance has numerous real-world applications, including:
- Navigation: The formula is used in navigation systems to calculate the distance between two points on a map.
- Surveying: The formula is used in surveying to calculate the distance between two points on a property.
- Physics: The formula is used in physics to calculate the distance traveled by an object under the influence of a constant acceleration.
Q: What are some tips and tricks for evaluating the formula for distance?
A: Some tips and tricks for evaluating the formula for distance include:
- Use a calculator: Use a calculator to simplify the equation and calculate the square root.
- Check your work: Double-check your work to ensure that you have calculated the squares, evaluated the sum, and calculated the square root correctly.
- Practice, practice, practice: Practice evaluating the formula for distance with different values of a and b to become more comfortable with the calculation.
Q: Can I use the formula for distance with negative values of a and b?
A: Yes, you can use the formula for distance with negative values of a and b. The formula will still work correctly, but you will need to take into account the direction of the distance.
Q: Can I use the formula for distance with non-integer values of a and b?
A: Yes, you can use the formula for distance with non-integer values of a and b. The formula will still work correctly, but you will need to use a calculator to simplify the equation and calculate the square root.
Conclusion
In conclusion, the formula for distance is a fundamental concept in mathematics that has numerous real-world applications. By understanding the formula and avoiding common mistakes, you can accurately calculate the distance between two points in a coordinate plane.