Question

Fill in the blanks!

Use the Pythagorean theorem to find the length of the hypotenuse, c.
Pythagorean theorem:
a^(2) + b^(2) = c^(2)
7^(2) + 24^(2) = c^(2)
_ + 576 = c^(2)
_ = c^(2)
\sqrt(625) = \sqrt(c^(2))
(underline)+ 25 = c
c = _ ft
Distance is always positive

Answer 1

To find the length of the hypotenuse \( c \) using the given information, let's fill in the blanks step by step:

1. Start with the Pythagorean theorem:

\[
a^2 + b^2 = c^2
\]

2. Substitute the given values:

\[
7^2 + 24^2 = c^2
\]

3. Calculate \( 7^2 \) and \( 24^2 \):

\[
7^2 = 49
\]
\[
24^2 = 576
\]

4. Substitute these values into the equation:

\[
49 + 576 = c^2
\]

5. Fill in the blanks:

- First blank: **49**
- Second blank: \( c^2 = 625 \)

6. Now, we will find \( c \):

\[
\sqrt{625} = \sqrt{c^2}
\]

7. Therefore, \( c \) is given by:

\[
c = 25 \text{ ft}
\]

So, the filled-in values are:

- \( 49 + 576 = c^2 \)
- \( c^2 = 625 \)
- \( c = 25 \text{ ft} \)

Distance is always positive, thus \( c = 25 \) ft is the final answer.