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In ΔTUV, v = 77 cm, u = 72 cm and ∠U=69°. Find all possible values of ∠V, to the nearest 10th of a degree.

User Bidby
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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.

User Abs
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