Answer:
The correct answer is the third option that is [tex](3.2)^2+(2.4)^2=(c)^{2}[/tex]
Step-by-step explanation:
An image is attached with it.
Lets say that [tex]AB[/tex] is the wall and[tex]AC[/tex] measuring [tex](c)[/tex] feet is the ladder length.
Now as Joe is climbing on it.
It moves horizontally [tex]2.4\ ft[/tex] taking it as [tex]x-axis[/tex] direction from the base [tex]C[/tex] then it also climb upward [tex]3.2\ ft[/tex] considering it as [tex]y-axis[/tex].
We see that the situation where we have drawn the ladder and the support (wall) it forms a right angled triangle.
So for this, the ladder is equivalent to the hypotenuse of the triangle.
And from Pythagoras formula for a right angled triangle we know that:
[tex](Hypotenuse)^2 = (Base)^2+(Perpendicular)^2[/tex]
Here the base [tex]=2.4\ ft[/tex] and perpendicular [tex]=3.2\ ft[/tex].
So the hypotenuse/ladder which is [tex](c)[/tex].
[tex](c)^2=(2.4)^2+(3.2)^2[/tex]
The situation which can be used to find how far Joe has climbed up the ladder = [tex](c)^2=(2.4)^2+(3.2)^2[/tex]
