In ΔMNO, o = 6.4 cm, n = 1.9 cm and ∠N=69°. Find all possible values of ∠O, to the nearest 10th of a degree.

To solve this problem, we will use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

1. First, we can find the value of ∠M using the Law of Sines. We have:

   sin(∠M) = n * sin(∠N) / o

   Substituting the given values:

   sin(∠M) = 1.9 * sin(69°) / 6.4

   ∠M = arcsin(1.9 * sin(69°) / 6.4)

2. To find ∠O, we subtract the sum of ∠M and ∠N from 180° (since the sum of angles in a triangle is 180°).

   ∠O = 180° - ∠M - ∠N

3. However, there is also a possibility that ∠M is obtuse. In this case, ∠M = 180° - arcsin(1.9 * sin(69°) / 6.4). Then, we can find ∠O using the same formula as in step 2.

So, there are two possible values for ∠O, depending on whether ∠M is acute or obtuse.