Question

Kyle is drawing a triangle on poster board. The first segment he draws is 11 inches in length, and the second segment is 14 inches long. The measure of the angle between those two segments is 65°. Which best describes the length of the third segment?

Answer 1

less than 25 inches

The sum of any two sides of a triangle must be greater than than the third side.

Since 11 + 14 = 25, the third segment must be less than 25 inches

The correct answer is less than 25 inches.

Answer 2

Using the law of cosines we can solve for the length of the third side:

a^2 = 11^2 + 14^2 -2*11*14*cos(65)

a^2 = 186.8336

The third side is 13.67 inches long. ( Round the answer as needed)

The answer would be less than 25 inches.