Final answer:
Using the Law of Sines, we can calculate the possible values of ∖V in the triangle by substituting known side lengths and angle ∖U. There may be two solutions, an acute angle and its supplementary obtuse angle. The final values will be rounded to the nearest 10th of a degree.
Step-by-step explanation:
To find the possible values of ∖V in ∆TUV, we can use the Law of Sines, which states that the ratios of the lengths of sides to the sines of their opposite angles are constant in any triangle. Therefore, v/sin(V) = u/sin(U). Given u = 72 cm, v = 77 cm, and ∖U = 69°, we can substitute these values into the formula. After calculating sin(U), we can solve for sin(V) and find ∖V. Remember, there can be two possible angles, so we must check for an obtuse angle if the first solution gives an acute angle by subtracting the acute angle from 180°. Finally, we can round our answer to the nearest 10th of a degree as requested.