To find the length of the missing leg \( b \) in a right triangle, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.
In your case, you have:
- One leg \( a = 4 \) m
- The other leg \( b \) (which is unknown)
- The hypotenuse \( c = 7 \) m
Plugging in the values, we get:
\[ 4^2 + b^2 = 7^2 \]
Calculating the squares:
\[ 16 + b^2 = 49 \]
Next, isolate \( b^2 \):
\[ b^2 = 49 - 16 \] \[ b^2 = 33 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{33} \approx 5.744 \]
Rounding to the nearest tenth, the length of the missing leg \( b \) is approximately:
\[ b \approx 5.7 , \text{m} \]
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