What are these equations supposed to represent, and where did they come from?

This looks like gobbledygook, tell us what you are trying to do and why.Distance = 80m, Time = 1.67 seconds

Upper height of target = 1.8m - 0.6m = 1.2m

Lower height of target = 1.8m + 0.6m = 2.4m

I did:

distance = rate*time

80m = rate*1.67 seconds

rate = 48m/s

then using t = 1.67 seconds, and v = 48m/s

Lower limit:

48sin(theta)(1.67) - 5(1.67)^2 = 1.2m

theta = 10.87 degrees

Upper limit:

48sin(theta)(1.67) - 5(1.67)^2 = 2.4m

theta = 11.79 degrees

I am not sure if this is the right way to do this question.

Also what course is this set as homework for, you have posted it Pre-Algebra and Algebra. If so you must have been given some background information that we don't have.

CB