To find the length of the missing leg (let's call it leg \(b\)) of a right triangle given the lengths of the other two legs (80 m and 64 m), we can use the Pythagorean theorem. The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
Where:
- \(c\) is the length of the hypotenuse,
- \(a\) and \(b\) are the lengths of the legs.
In your case, it seems like you have two legs (assuming 80 m and 64 m) and need to find the third leg. Let's assume 80 m is one leg and 64 m is the other leg.
The formula can be rearranged based on which leg you are missing:
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If 80 m is the hypotenuse: \[ b^2 + 64^2 = 80^2 \] \[ b^2 + 4096 = 6400 \] \[ b^2 = 6400 - 4096 \] \[ b^2 = 2304 \] \[ b = \sqrt{2304} \approx 48.0 \text{ m} \]
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If 64 m is the hypotenuse: \[ 80^2 + b^2 = 64^2 \] This would not make sense because \(80 > 64\).
Thus, the only scenario where \(b\) is missing is when it's the shorter leg, which is 48.0 m.
So, the length of the missing leg \(b\) is approximately 48.0 m (rounded to the nearest tenth).
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