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:
\[ \boxed{25} \]
1 answer