Answer:
The distance between the boats is [tex]50\ mi[/tex]
Step-by-step explanation:
we know that
The Pythagoras Theorem states that
In a right triangle
[tex]c^{2}=a^{2}+b^{2}[/tex]
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
[tex]a=12+18=30\ mi[/tex]
[tex]b=16+24=40\ mi[/tex]
substitute the values
[tex]c^{2}=30^{2}+40^{2}[/tex]
[tex]c^{2}=2,500[/tex]
[tex]c=50\ mi[/tex]
