The measures of two sides of a triangle are 5.2 and 8.1. Determine the range of values for the third side of the triangle.(1 point)
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To determine the range of values for the third side of the triangle, we need to use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the lengths of the two given sides as a and b:
a = 5.2
b = 8.1
Now, we can express the inequality using these variables:
|a - b| < c < a + b
Substituting the given values:
|5.2 - 8.1| < c < 5.2 + 8.1
|-2.9| < c < 13.3
2.9 < c < 13.3
Therefore, the range of values for the third side of the triangle is 2.9 to 13.3.