To find the length of the missing leg \( b \) in a right triangle with legs measuring 6 cm and 5 cm, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Since you have provided two legs and are looking for the missing leg \( b \), we will assume either \( 6 \) cm or \( 5 \) cm is a leg and you want to find the missing side using the other as a reference.
Assuming \( a = 6 \) cm and \( b = 5 \) cm:
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If you want to find the hypotenuse \( c \): \[ c^2 = 6^2 + 5^2 = 36 + 25 = 61 \] \[ c = \sqrt{61} \approx 7.81 \text{ cm} \]
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If you want to find the length of the missing leg \( b \) using \( c \) as the hypotenuse, you would rearrange the equation:
- Let's consider \( c \) is known and is, for instance, \( 7 \) cm: \[ 6^2 + b^2 = c^2 \] \[ 36 + b^2 = 7^2 \] \[ 36 + b^2 = 49 \] \[ b^2 = 49 - 36 \] \[ b^2 = 13 \] \[ b \approx \sqrt{13} \approx 3.6 \text{ cm} \]
Please clarify whether you want to find the hypotenuse or the other leg, and specify if additional information is available (e.g., if there is another leg or the hypotenuse).
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