Use the image to answer the question.
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.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
m^2+n^2=??
Since the Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, we can conclude that:
m^2 + n^2 = ?
Based on the given information and the image, we cannot determine the lengths of the sides in the triangle. Therefore, we cannot calculate the value of m^2 + n^2.
To determine the relationship of the sides in this triangle based on the Pythagorean Theorem, we need to identify the sides of the triangle first.
From the given labeling, we can see that side MN is labeled 'o', side NO is labeled 'm', and side OM is labeled 'n'.
Now, according to the Pythagorean Theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the angle measurements are not given, but we can conclude that triangle MON is a right-angled triangle because angle N measures 62 degrees and angle M measures 28 degrees, and the sum of these two angles is 90 degrees.
So, in triangle MON, 'NO' is the hypotenuse ('m' in the question) and 'NM' and 'OM' are the other two sides ('o' and 'n', respectively).
Therefore, based on the Pythagorean Theorem, the relationship of the sides in this triangle can be expressed as:
m^2 = o^2 + n^2
From the given information, we can determine that angle M measures 28 degrees and angle N measures 62 degrees in triangle MON.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides.
However, the information provided in the question does not indicate that triangle MON is a right triangle, so we cannot directly apply the Pythagorean Theorem.