To determine the range of values for the third side of a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with sides \(a\), \(b\), and \(c\):
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
In your case, let the two given sides be \(a = 5.2\) and \(b = 8.1\), and let \(c\) be the length of the third side.
We can apply the triangle inequality as follows:
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\(5.2 + 8.1 > c\) \[ 13.3 > c \quad \Rightarrow \quad c < 13.3 \]
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\(5.2 + c > 8.1\) \[ c > 8.1 - 5.2 \quad \Rightarrow \quad c > 2.9 \]
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\(8.1 + c > 5.2\) \[ c > 5.2 - 8.1 \quad \Rightarrow \quad c > -2.9 \] (This condition is always satisfied, as \(c\) is a positive length.)
Combining the relevant inequalities, we find: \[ 2.9 < c < 13.3 \]
Thus, the range of values for the third side \(n\) is: \[ \boxed{2.9 < n < 13.3} \]