a man walks 3.00 mi due east, then turns and walks 2.00 mi due north. How far is he from the starting point?
what is sqrt(3^2+2^2)
13
To find the distance between the man's final position and his starting point, we can use the Pythagorean theorem.
Step 1: Plot the man's movements on a coordinate plane.
- Let's assume the starting point is at coordinates (0,0).
- The man walks 3.00 miles due east, so his new position would be (3,0).
- Then, he turns and walks 2.00 miles due north from his new position, which brings him to (3,2).
Step 2: Calculate the distance using the Pythagorean theorem.
- The Pythagorean theorem states that for any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- In this case, the man's displacement forms a right triangle. The sides of the triangle represent his eastward and northward movements.
- The eastward movement is the base of the triangle with a length of 3.00 miles, while the northward movement is the height with a length of 2.00 miles.
- Therefore, using the Pythagorean theorem, the distance from the starting point to the man's final position is given by:
distance = √(3.00^2 + 2.00^2)
= √(9.00 + 4.00)
= √13.00
≈ 3.61 miles
Hence, the man is approximately 3.61 miles away from his starting point.