A man walks 6 km east, then 8 km north. How far is he from the starting point?

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Question: A man walks 6 km east, then 8 km north. How far is he from the starting point?

Options:

Correct Answer: 10 km

Solution:

Using the Pythagorean theorem, the distance is √(6² + 8²) = 10 km.

A man walks 6 km east, then 8 km north. How far is he from the starting point?

A man walks 6 km east, then 8 km north. How far is he from the starting point?

Step 1: Understand that the man walks in two directions: east and north.
Step 2: Visualize the path as a right triangle, where one side is the distance walked east (6 km) and the other side is the distance walked north (8 km).
Step 3: Identify the two sides of the triangle: one side is 6 km (east) and the other side is 8 km (north).
Step 4: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the distance from the starting point) is equal to the sum of the squares of the other two sides.
Step 5: Calculate the squares of the two sides: 6² = 36 and 8² = 64.
Step 6: Add the squares together: 36 + 64 = 100.
Step 7: Take the square root of the sum to find the hypotenuse: √100 = 10.
Step 8: Conclude that the man is 10 km away from the starting point.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Distance Calculation – Understanding how to calculate the straight-line distance between two points using coordinates.