Question

Pythagorean Theorem. I need help please!!!!!

Answer 1

The hikers started at point S.
The first hiker went 2 miles east and 1 mile north to point A.
The second hiker went 1 mile west and 3 miles south to point B.
See the figure below.

                                                              A
                                                              I
                           1 mile                         I    1 mile
                          I---------S------------------I
                          I                    2 miles
                          I
                          I
            3 miles   I
                          I
                          I
                          B


Now we need to see how much east and how much north hiker B is from hiker A.


                                                            A
                                                              I
                           1 mile                         I    1 mile
                          I---------S------------------I
                          I                    2 miles   I
                          I                                   I
                          I                                   I
            3 miles   I                                   I   3 miles
                          I                                   I
                          I                                   I
                          B----------------------------I
                                         3 miles

From point B go 3 miles east, then 3 + 1 = 4 miles north to point B.
The distance between the hikers is the hypotenuse of a triangle with legs of lengths 3 and 4.

3^2 + 4^2 = d^2

9 + 16 = d^2

d^2 = 25

d = 5

The distance between the hikers is 5 miles.