Angela and Johnnie each leave the park to head back to their houses after playing basketball. Angela walks 1.3 miles South from the Park and Johnnie walks 2.2 miles east. If Angela and Johnnie each walk in straight paths, how many miles apart would they be when they each reach their own house? Round your final answer to the nearest tenth of a mile.

To find out how far apart Angela and Johnnie are when they reach their respective houses, we can use the Pythagorean theorem because they have traveled perpendicular paths (south and east).

According to the Pythagorean theorem, in a right-angled 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 lengths of the other two sides.

So, if we let

�

=

1.3

a=1.3 miles (Angela's distance south) and

�

=

2.2

b=2.2 miles (Johnnie's distance east), then the distance between them,

�

c, would be:

�

=

�

2

+

�

2

c=

a

2

+b

2

Substituting the given values:

�

=

(

1.3

)

2

+

(

2.2

)

2

c=

(1.3)

2

+(2.2)

2

�

=

1.69

+

4.84

c=

1.69+4.84

�

=

6.53

c=

6.53

�

≈

2.6

c≈2.6

So, when rounded to the nearest tenth of a mile, Angela and Johnnie would be approximately 2.6 miles apart when they each reach their own house.