what is the value of the cosine of v to the nearest hundredth.

First, draw the triangle as follows to illustrate the parts of the given triangle:
Since the triangle is right, we may use the trigonometric identity to find cos V. The computation for the cos V is as follows:
[tex]\cos V=\frac{adjacent\text{ side}}{hypothenuse}[/tex]Substitute the values of the given such that the hypothenuse is the longest side of the triangle, UV.
[tex]\cos V=\frac{WV}{VU}=\frac{40}{41}\approx0.98[/tex]