To find the unknown side length in the triangle, we can apply 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 remaining side.
Let's denote the unknown side as \( c \), and we have the following three sides of the triangle:
- \( a = 20 \)
- \( b = 30 \)
- \( c = ? \)
According to the triangle inequality theorem, we have the following inequalities:
-
\( a + b > c \): \[ 20 + 30 > c \implies 50 > c \implies c < 50 \]
-
\( a + c > b \): \[ 20 + c > 30 \implies c > 10 \]
-
\( b + c > a \): \[ 30 + c > 20 \implies c > -10 \quad \text{(this inequality is always true since \( c \) must be positive)} \]
From these inequalities, we can conclude that:
\[ 10 < c < 50 \]
Thus, the unknown side \( c \) could be any value in the range (10, 50). If you have specific conditions or constraints regarding this triangle (e.g., it’s a right triangle, an isosceles triangle, etc.), please provide that information to calculate \( c \) more precisely. Otherwise, we cannot determine a unique value for \( c \) from the given information alone.