In triangle $ABC$, side $a$ is $11$ ft and side $b$ is $13$ ft. Which of the following could be the length of side $c$ if angle $C$ is opposite side $c$ and angle $C$ is the largest angle in the triangle?

• A. $18$ ft
• B. $11$ ft
• C. $15$ ft
• D. $13$ ft

Answer: (C)

Verified step by step guidance

1. Recall that in any triangle, the largest angle is opposite the longest side. Since angle C is the largest angle, side c must be the longest side of the triangle.
2. Given sides a = 11 ft and b = 13 ft, side c must be longer than both 11 ft and 13 ft to satisfy the condition that angle C is the largest angle.
3. Use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. So, for side c, the following must hold: \(a + b > c\), \(a + c > b\), and \(b + c > a\).
4. Substitute the known values into the inequalities: \$11 + 13 > c\( which simplifies to \)24 > c\(, and also \)c > 13$ since c must be the longest side.
5. From these inequalities, side c must be greater than 13 ft but less than 24 ft. Among the given options, only 15 ft satisfies this condition, making it a possible length for side c.