A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.

Question

Side m
is approximately 6.1 units, side n
is approximately 11.48 units, and side o
is 13 units. What is the length of the hypotenuse of this triangle? How do you know?

(1 point)
Responses

The length is approximately 11.48 units because it forms the right angle.
The length is approximately 11.48 units because it forms the right angle.

The length is approximately 11.48 units because it is the middle length.
The length is approximately 11.48 units because it is the middle length.

The length is approximately 6.1 units because the hypotenuse is the shortest side.
The length is approximately 6.1 units because the hypotenuse is the shortest side.

The length is 13 units because the hypotenuse is the longest side

Answer 1

The correct response is:

The length is 13 units because the hypotenuse is the longest side.

In a triangle, the hypotenuse is the longest side, which is opposite the right angle. Given the side lengths provided (approximately 6.1 units, 11.48 units, and 13 units), the side measuring 13 units is indeed the longest. From the context, since we know two angles (62 degrees and 28 degrees) and no right angle is mentioned, we can conclude that if it were a right triangle, the side opposite the right angle (hypotenuse) would be the longest side. Hence, the hypotenuse is confirmed to be 13 units.