A 6 ft man stands by a 30 ft tower and casts a 10 ft shadow. How long is the shadow cast by the tower and what time is it?

6/10 = 30/x

x = 50

tan 30.96°

Since our measurements may not be exact, let's just call it 30°. Since there are 360° in a circle, the sun is up 1/12 of a day, or 2 hours.

Now for the stupid part. Depending on the latitude and day of the year, the time of day will vary. If we stipulate we're on the equator, and sunrise and sunset both occur at 6:00, then it's either

8:00 am or 4:00 pm.

I get so tired of problems where there is so much unspecified that it is impossible to respond in a meaningful manner...

The only thing we can really say is that it's probably not cloudy (at least in the part of the sky where the sun is shining on the tower and man).