Question

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Part 1
Use the Pythagorean Theorem to find the missing length in the right triangle.
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Question content area top right
Part 1
7
24
c
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Part 1
  
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Answer 1

To find the missing length \( c \) in the right triangle using the Pythagorean Theorem, we use the formula:

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

where \( a \) and \( b \) are the lengths of the two legs of the triangle, and \( c \) is the length of the hypotenuse.

In this case, the lengths of the legs are \( 7 \) and \( 24 \). Using the theorem:

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

Calculating \( 7^2 \) and \( 24^2 \):

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

Now, we add these two results together:

\[
c^2 = 49 + 576 = 625
\]

Now, to find \( c \), we take the square root of \( 625 \):

\[
c = \sqrt{625} = 25
\]

Thus, the missing length \( c \) is:

\[
\boxed{25}
\]