To find the length of the missing leg, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. The formula is:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the legs.
From your question, it seems you have two lengths, 9.9 miles and 7.2 miles, but it's not clear which one is the hypotenuse or if one is the missing leg. If we assume that 9.9 miles is the hypotenuse:
Let \( a = 7.2 \) miles (one leg) and \( c = 9.9 \) miles (hypotenuse). We need to find \( b \) (the missing leg).
Using the Pythagorean theorem:
\[ 7.2^2 + b^2 = 9.9^2 \]
Calculating the squares:
\[ 51.84 + b^2 = 98.01 \]
Subtract \( 51.84 \) from both sides:
\[ b^2 = 98.01 - 51.84 \] \[ b^2 = 46.17 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{46.17} \approx 6.8 \]
Thus, the length of the missing leg is approximately 6.8 miles when rounded to the nearest tenth.
If you meant something different regarding the configuration of the triangle, please provide more details!
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