To find the length of the missing side in a right triangle with a height of 10 and a length of 24, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse and \( a \) and \( b \) are the legs of the triangle.
Assuming the height (10) and length (24) represent the two legs, we can set:
- \( a = 10 \)
- \( b = 24 \)
Now we can solve for \( c \):
\[ c^2 = a^2 + b^2 \] \[ c^2 = 10^2 + 24^2 \] \[ c^2 = 100 + 576 \] \[ c^2 = 676 \]
Now, take the square root to find \( c \):
\[ c = \sqrt{676} = 26 \]
If either 10 or 24 is considered one of the legs, then we can find the third side as well. If we consider 24 to be the hypotenuse, then we will use the Pythagorean theorem again to find the missing leg.
Assuming \( c = 24 \):
\[ c^2 = a^2 + b^2 \] \[ 24^2 = 10^2 + b^2 \] \[ 576 = 100 + b^2 \] \[ b^2 = 576 - 100 \] \[ b^2 = 476 \]
Now taking the square root to find \( b \):
\[ b = \sqrt{476} \approx 21.82 \quad (\text{rounded to two decimal places}) \]
So the length of the missing side, approximately, is:
- If considering height and length as legs: \( 26.00 \)
- If considering the height as one leg and the given length as the hypotenuse, the missing leg is approximately \( 21.82 \).
You can confirm which scenario fits your triangle configuration best!
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