To find the length of the missing side (let's call it \( a \)) of a right triangle given the lengths of the other two sides (15 and 9), you can use the Pythagorean theorem. The theorem states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
- If 15 is the hypotenuse and 9 is one leg, you can set it up as follows:
\[ 9^2 + a^2 = 15^2 \]
Calculating the squares:
\[ 81 + a^2 = 225 \]
Now, solve for \( a^2 \):
\[ a^2 = 225 - 81 \] \[ a^2 = 144 \]
Now, take the square root of both sides:
\[ a = \sqrt{144} \] \[ a = 12 \]
So in this case, the missing leg (\( a \)) is 12.
- If instead, 15 is one leg and 9 is the other leg, we would set it up as:
\[ 15^2 + 9^2 = a^2 \]
Calculating the squares:
\[ 225 + 81 = a^2 \]
Now, solve for \( a^2 \):
\[ a^2 = 306 \]
Now, take the square root of both sides:
\[ a = \sqrt{306} \] \[ a \approx 17.44 \]
In conclusion:
- If 15 is the hypotenuse, the missing leg \( a \) is 12.
- If 15 is one leg, the missing side \( a \) is approximately 17.44.
You would need to clarify which side is the hypotenuse for a definitive answer.
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