How can I rearrange this for the angle?

[iamBevan]

also - The result I'm getting for d is 18587 - this is when I enter 427 for initial velocity, 45 for theta, and 9.81 for g - is this correct?

 

[Unrest]

To rearrange, use inverse operations to move things you don't want to the other side -

You're dividing the RHS by g, so multiply both sides by g
You're multiplying the RHS by v^2 so divide both sides by v^2
Then use the inverse sin function
etc.

To see if it's correct, compare the result to some other method for estimating the same thing, or even just your intuition.

 

[HallsofIvy]

I get 18586- with decimal part .o345...

To solve for $\theta$, "unpeel" what has been done:
$$d= \frac{v^2sin(2\theta)}{g}$$
so, multiplying both sides by g,
[tex]dg= v^2 sin(2\theta)[/itex]<br /> dividing both sides by $v^2$,<br /> $$\frac{dg}{v^2}= sin(2\theta)$$<br /> Taking the inverse sine (arcsin) of both sides<br /> (be careful- since sine is not one-to-one there is no "true" inverse- there are an infinite number of angles with the same sine- two between 0 and pi/2- and "arcsin" only gives one of them)<br /> $$arcsin\left(\frac{dg}{v^2}\right)= 2\theta$$<br /> and, finally, divide both sides by 2:<br /> $$\frac{1}{2}arcsin\left(\frac{dg}{v^2}\right)= \theta$$[/tex]

 

[iamBevan]

Thanks guys - that was a massive help.