Question

Find the unknown side length in the given triangle. Round to the nearest hundredth. One side is 20 and one side is 30 and the other is unknown

Answer 1

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:

1. \( a = 20 \)
2. \( b = 30 \)
3. \( c = ? \)

According to the triangle inequality theorem, we have the following inequalities:

1. \( a + b > c \):
\[
20 + 30 > c \implies 50 > c \implies c < 50
\]

2. \( a + c > b \):
\[
20 + c > 30 \implies c > 10
\]

3. \( b + c > a \):
\[
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.