Question

Two boats leave an island at the same time. One of the boats travels 12 miles east and then 16 miles north. The second boat travels 24 miles south and then 18 miles west. Use the pythagorean theorem to find the distance between the boats.

Answer 1

The distance between the boats is
`50\ mi`

Explanation:

we know that

The Pythagoras Theorem states that

In a right triangle

`c^(2)=a^(2)+b^(2)`

where

c is the hypotenuse

a and b are the legs

In this problem

Let

c ----> the distance between the boats

a -----> the horizontal distance between the boats

b -----> the vertical distance between the boats

`a=12+18=30\ mi`

`b=16+24=40\ mi`

substitute the values

`c^(2)=30^(2)+40^(2)`

`c^(2)=2,500`

`c=50\ mi`