Fill in the blanks!

Robert wants to hang a picture above his entertainment center. How long must a ladder be to reach a height of 13 feet if the bottom of the ladder is placed 3 feet from the base of the wall?

a^(2) + b^(2) = c^(2)
3^(2) + 13^(2) = c^(2)
9 + _ = c^(2)
\sqrt(178) = \sqrt(c^(2))
\sqrt(178) = c

Use a calculator to give an approximate number for the length.
c ~ _ ft

1 answer

Let's fill in the blanks step by step.

We start with the Pythagorean theorem:

a2+b2=c2

In this case, a is the distance from the wall (3 feet), and b is the height (13 feet). Therefore, we have:

32+132=c2

Calculating 132:

132=169

Now we can replace the blank in the equation with 169:

9+169=c2

Now we add:

9+169=178

So we have:

c2=178

Now take the square root to find c:

c=178

Using a calculator to compute:

c13.34

So we fill in the last blank:

c ~ 13.34 ft