Fill in the blanks!

Question

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

Answer 1

Let's fill in the blanks step by step.

We start with the Pythagorean theorem:

$$a^2+b^2=c^2$$

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

$$3^2+{13}^2=c^2$$

Calculating ${13}^2$:

$${13}^2=169$$

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

$$9+169=c^2$$

Now we add:

$$9+169=178$$

So we have:

$$c^2=178$$

Now take the square root to find $c$:

$$c=\sqrt{178}$$

Using a calculator to compute:

$$c\approx 13.34$$

So we fill in the last blank:

c ~ 13.34 ft