In order to find the length of v in ΔUVW, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. This can be expressed as:
a/sin A = b/sin B = c/sin C
Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.
In ΔUVW, we are given the lengths of two sides (w and v) and the measure of the angles opposite those sides (m∠W and m∠U). We can use the Law of Sines to find the length of v:
v/sin U = w/sin W
v = (w/sin W) * sin U
Substituting the given values, we get:
v = (1.4 cm / sin 63°) * sin 29°
Using a calculator, we find that v = 2.72 cm to the nearest hundredth of a centimeter. Rounding to the nearest 10th of a centimeter, we get v = 2.7 cm.
Therefore, the length of v in ΔUVW is approximately 2.7 cm to the nearest 10th of a centimeter.