Step-by-step explanation:
To determine the range of possible values for the third side of 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.
Given that the two known sides of the triangle measure 10 cm and 16 cm, let's denote the length of the unknown third side as x.
Based on the triangle inequality theorem, we can write the following inequality:
10 + 16 > x
Simplifying the inequality, we get:
26 > x
Therefore, the range of possible values for the third side of the triangle is x < 26.
However, since the triangle is an acute triangle, we also know that the sum of the lengths of any two sides of an acute triangle must be greater than the length of the third side.
Considering this additional condition, we can write the following inequality:
10 + x > 16
Simplifying the inequality, we get:
x > 6
Therefore, the range of possible values for the third side of the triangle is x > 6.
Combining both inequalities, we can conclude that the range of possible values for the third side of the triangle is 6 < x < 26.
