To analyze a right triangle with sides of lengths 11 and 10, we need to clarify whether these sides are the legs (the two shorter sides) or if one of them is the hypotenuse (the longest side opposite the right angle).
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If 11 and 10 are the legs:
- To find the hypotenuse \( c \), we can use the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where \( a = 10 \) and \( b = 11 \). \[ c = \sqrt{10^2 + 11^2} = \sqrt{100 + 121} = \sqrt{221} \approx 14.87 \]
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If 11 is the hypotenuse and 10 is one of the legs:
- Let's do the same with the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] Here, \( c = 11 \) and we can take \( b = 10 \). We need to find \( a \): \[ a^2 + 10^2 = 11^2 \] \[ a^2 + 100 = 121 \] \[ a^2 = 21 \] \[ a = \sqrt{21} \approx 4.58 \]
So, depending on how the sides are positioned in the triangle:
- If 10 and 11 are the legs, the hypotenuse is approximately 14.87.
- If 11 is the hypotenuse and 10 is one leg, the other leg would be approximately 4.58.