A man walks 10 km east, then 5 km north. Find distance from start.

Calculating Distance: A Simple Guide Using the Pythagorean Theorem

Imagine a hiker navigating a challenging trail, or a delivery driver plotting the most efficient route. Both rely on accurately calculating distances. This blog post will guide you through a simple distance calculation using the Pythagorean Theorem.

The Problem: A Man's Walk

Let's tackle a common problem: A man walks 10 km east, then 5 km north. What is the straight-line distance from his starting point?

Understanding Distance and Displacement

Distance is the total length of the path traveled. In our example, the distance is 10 km + 5 km = 15 km. However, distance doesn't tell us the straight-line path back to the starting point.

Displacement is the straight-line distance between the starting and ending points, considering the direction. This is what we want to calculate.

The Pythagorean Theorem

The Pythagorean Theorem helps us find the displacement when we have a right-angled triangle. The theorem states: a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides (legs) of the right-angled triangle, and 'c' is the length of the longest side (hypotenuse).

Solving the Problem: Visualizing and Calculating

Let's visualize the man's walk:

(Insert a diagram here showing the man walking 10km east and then 5km north, forming a right-angled triangle. The hypotenuse represents the straight-line distance.)

Now let's apply the Pythagorean Theorem:

1. a = 10 km (eastward distance)
2. b = 5 km (northward distance)
3. c² = a² + b² = 10² + 5² = 100 + 25 = 125
4. c = √125 ≈ 11.18 km

Therefore, the straight-line distance from the man's starting point is approximately 11.18 km.

Real-World Applications

The Pythagorean Theorem is crucial in many fields: navigation systems, surveying land, construction, and even video game development!

Conclusion

We successfully calculated the straight-line distance using the Pythagorean Theorem. Remember, distance and displacement are different; displacement considers the shortest distance between start and end points. Practice more problems to master this essential concept!

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Calculating Distance: A Simple Guide Using the Pythagorean Theorem

Imagine a hiker navigating a challenging trail, or a delivery driver plotting the most efficient route. Both rely on accurately calculating distances. This blog post will guide you through a simple distance calculation using the Pythagorean Theorem.

The Problem: A Man's Walk

Let's tackle a common problem: A man walks 10 km east, then 5 km north. What is the straight-line distance from his starting point?

Understanding Distance and Displacement

Distance is the total length of the path traveled. In our example, the distance is 10 km + 5 km = 15 km. However, distance doesn't tell us the straight-line path back to the starting point.

Displacement is the straight-line distance between the starting and ending points, considering direction. This is what we need to calculate.

The Pythagorean Theorem

The Pythagorean Theorem helps us find the displacement when we have a right-angled triangle. The theorem states: a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides (legs) of the right-angled triangle, and 'c' is the length of the longest side (hypotenuse).

Solving the Problem: Visualizing and Calculating

Let's visualize the man's walk:

Now, let's apply the Pythagorean Theorem:

1. a = 10 km (eastward distance)
2. b = 5 km (northward distance)
3. c² = a² + b² = 10² + 5² = 100 + 25 = 125
4. c = √125 ≈ 11.18 km (using a calculator)

Therefore, the straight-line distance from the man's starting point is approximately 11.18 km.

Real-World Applications

The Pythagorean Theorem is crucial in various fields: navigation systems, surveying land, construction, and even video game development!

Conclusion

We successfully calculated the straight-line distance using the Pythagorean Theorem. Remember, distance and displacement are different; displacement is the shortest distance between start and end points. Practice more problems to master this important concept! You can try problems with different directions or multiple legs to challenge yourself further.