Answer:
10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
[tex]a=12\ in, b=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the hypotenuse
[tex]c^{2}=a^{2} +b^{2}[/tex]
substitute
[tex]c^{2}=12^{2} +15^{2}[/tex]
[tex]c^{2}=369[/tex]
[tex]c=19.2\ in[/tex]
Second case
The given lengths are one leg and the hypotenuse
so
[tex]a=12\ in, c=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the other leg
[tex]b^{2}=c^{2} - a^{2}[/tex]
substitute
[tex]b^{2}=15^{2} - 12^{2}[/tex]
[tex]b^{2}=81[/tex]
[tex]b=9\ in[/tex]
Find the difference between the two possible lengths of the third side of the triangle
so
[tex]19.2-9=10.2\ in[/tex]
