Answer:
cos(z) = .3846153846 and angle z = 67.38°
Step-by-step explanation:
Side UV is corresponding to side YX. Side VW is corresponding to side YZ. Side UW is corresponding to side XZ.
Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that. So side YX is
We are next told that side VW is 39, so side YZ is
In order to find the cos of angle z, we need the adjacent side, which is side XZ. Side XZ is 3/5 of side UW. Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:
and
so
UW = 15
Now we can say that side XZ is
The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:
which divides to
cos(z) = .3846153846
If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that
angle z = 67.38°