Question

In ΔMNO, NO = 15, OM = 18, and MN = 10. Which list has the angles of ΔMNO in order from largest to smallest?

Answer 1

To find the order of the angles in triangle MNO from largest to smallest, use the Law of Cosines to calculate the angles

Step-by-step explanation:

To determine the order of the angles in triangle MNO from largest to smallest, we need to consider the side lengths of the triangle. In triangle MNO, NO = 15, OM = 18, and MN = 10.

We can use the Law of Cosines to find the angles:

Using the Law of Cosines, angle N = arccos((18^2 + 10^2 - 15^2) / (2 * 18 * 10))

Using the Law of Cosines, angle O = arccos((15^2 + 10^2 - 18^2) / (2 * 15 * 10))

Using the Law of Cosines, angle M = arccos((15^2 + 18^2 - 10^2) / (2 * 15 * 18))

Now, we can compare the angles to determine the order:

The largest angle is angle N

The next largest angle is angle O

The smallest angle is angle M