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