A man walks 3 miles due east, then 4 miles due north, then five miles due east. How far is he from his starting point?
if he starts at (0,0), then he winds up at (8,4).
So, he is then √80 miles from home.
To find the distance from his starting point, we can use the Pythagorean theorem. Let's break down the steps to get the answer:
1. Draw a diagram: Draw a diagram with a starting point, and mark the directions and distances the man walked. Label the starting point as A.
2. Break down the distances: The man walked 3 miles due east from point A, so mark the endpoint of this path as B. From point B, the man walks 4 miles due north, which takes him to point C. Finally, the man walks 5 miles due east from point C, and this brings him to the endpoint, which we'll call point D.
3. Calculate the distances: Now, we need to calculate the distances AB, BC, and CD. Since the man walked due east for 3 miles, AB has a length of 3 miles. Similarly, BC is 4 miles, and CD is 5 miles.
4. Use the Pythagorean theorem: The Pythagorean theorem states that in a right 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 other two sides. In this case, AB and BC form a right triangle at point B, so we can use the theorem to find the distance BD.
By applying the theorem, we find that BD^2 = AB^2 + BC^2.
Plugging in the values, BD^2 = 3^2 + 4^2.
Simplifying, BD^2 = 9 + 16 = 25.
Taking the square root of both sides, we find BD = sqrt(25) = 5.
5. Final answer: The man is 5 miles away from his starting point, which is the length of BD.
Therefore, the man is 5 miles from his starting point.