Final answer:
The range of values for the length of the third side in the triangle is 21 < hj < 75.
Step-by-step explanation:
To find the range of values for the length of the third side in the triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's consider the two sides hi = 48 and ij = 27. So the range of values for the length of the third side, hj, would be:
hj < hi + ij and hj > |hi - ij|
Substituting the values, we get:
hj < 48 + 27 = 75
hj > |48 - 27| = 21
Therefore, the range of values for the length of the third side is:
21 < hj < 75 (option c)