Help, I'm not sure where I went wrong!

Question

babynini · Answer

attachment

loser66 · Answer

Show your work, I can check where you went wrong. :)

babynini · Answer

okies, give me just a moment to type it all up

babynini · Answer

7000 = [(211)^2 sin(2theta)]/32

[7000(32)]/(2100^2) = sin 2theta

0.05079 = sin 2theta

correct so far?

babynini · Answer

which means that 
2theta = (approximately) 2.9115

radar · Answer

looking at the entered answer, you messed up the comma.

babynini · Answer

what comma?

babynini · Answer

ooh because there's two answers.

radar · Answer

Looking at your link, the comma between the 6 and 8

babynini · Answer

there's two answers, is why.

babynini · Answer

But maybe they just want one o.0

babynini · Answer

umm, yeah it didn't like just 1.46

babynini · Answer

It wants it at three decimal places but 1.4557 is rounded to 1.46 :|
maybe 1.456?

radar · Answer

They want it rounded to three decimal places.  Let me read it again, I don't see how they can expect two answers.

babynini · Answer

Ok, I got it now :)
It wanted 1.456,88.5442

babynini · Answer

1.456 being one answer, and 88.544 being the other.

babynini · Answer

I assumed they wanted two answers because it said "separate answers by comma." Those sketchy program writers.

radar · Answer

I see the angle you solved for the 1.456 degree, how do you get the 88.544, that is almost straight up and I can't see how a range of 7000 ft is obtained!!

babynini · Answer

so theta = 1.4557
and then we take that number and subtract it from 180

babynini · Answer

and that gives us 88.5442, another angle at which we can get the same distance, but a different arch

radar · Answer

Well my calculator gave me an angle theta of 1.456 degree,  but there would be another at 178.544 degree.

radar · Answer

|dw:1431397533576:dw|

radar · Answer

That would give you another 7000 ft in a different direction.

babynini · Answer

Ok, remember when we had 
2theta = sin^-1(0.05079) ?
then we got
2theta = (approximately) 2.9115

divide that by two and we got our theta of = 1.456
If we take that same number, 2.9115, and subtract it from 180 we get our other angle.

2theta = 180 - 2.9115

2theta = 177.088

so theta = 88.544

babynini · Answer

Does that make sense? :)

radar · Answer

No, the angle as you computed is 1.456 degree,, an  angle of 88 which is almost 90 is like shooting the gun straight up.|dw:1431397962202:dw|

radar · Answer

|dw:1431398056662:dw|
See the difference.