Aprojectile is launched from the ground at an angle of theta above the horizontal with an initial speed of v in ft/s. the range (the total distance traveled by the projectile over level ground) of the projectile is approximated by the equation . find the launch angle of a projectile with an initial speed of 85ft/s and a range of 170 ft.

Step-by-step explanation:

The formula you wrote has the fraction the other way around. You can find that the range of a projectile is in reality approximated by the equation , where we will use ft for distances.

From the given equation we have then , which means since the arcsin is the inverse function of the sin.

Since we have x = 170 ft and  v = 85 ft/s, we can substitute these values from the equation written, and we will have , and from now on we have just to use a calculator, obtaining