To find the length of the missing leg in a right triangle when given the lengths of the two other legs, you can use the Pythagorean theorem. The theorem states:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs, and
- \(c\) is the length of the hypotenuse.
In your case, it seems you're looking for the length of the missing leg \(b\), and you have one leg as 7 cm and the other as 3 cm.
Since we don’t know whether the 7 cm or the 3 cm is the hypotenuse, let's consider both scenarios:
-
If 7 cm is the hypotenuse: \[ 7^2 = 3^2 + b^2 \] \[ 49 = 9 + b^2 \] \[ b^2 = 49 - 9 \] \[ b^2 = 40 \] \[ b = \sqrt{40} \approx 6.3 \text{ cm} \]
-
If 3 cm is the hypotenuse (which is not possible in this case as 3 cm < 7 cm): \[ 3^2 = 7^2 + b^2 \] \[ 9 = 49 + b^2 \quad (not possible) \]
Since the 3 cm cannot be the hypotenuse, the valid calculation shows that if 7 cm is the hypotenuse, the missing leg \(b\) is approximately 6.3 cm when rounded to the nearest tenth.
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