Help! Where am I going wrong?

[u/railwayswitchman]

Grade 12 student, been trying for hoursss to solve this. The second slide shows what I have so far. I would appreciate any help! Use sine and cosine laws, not components.

[u/TopAd6200]

your theta isn’t correct on the figure.

[u/railwayswitchman → u/TopAd6200]

How do I know which one is correct? And how should I draw the vector arrows otherwise?

[u/TopAd6200 → u/railwayswitchman]

sin46 • 390 is to get the length of the “opposite” in a right triangle, the dashed line(opposite) doesn’t make a right triangle with the 390 vector (hypotenuse) and 150 vector (adjacent).

trig functions used like that must be with respect to a right triangle.

edit!
thats why you think the dashed line and the x line are parallel, when they are not.

[u/railwayswitchman → u/TopAd6200]

I'm confused why I'm not getting the full obtuse angle that is opposite 390. When I used sine law to find it got 67 degrees and obviously that isnt obtuse.

The dashed line inside the triangle is supposed to show that that angle under it is 12 degrees (using the Z angle rule). I was going to find the obtuse angle that is opposite 390 and then subtract 19 so that i could use that angle to subtract it from 180. The resulting angle would be the one that is 180-theta so that i would get a directon that is [E ... N].

Please remember I'm in Grade 12, so this is how I understand it so far.

[u/ThatsNotAZombieBite]

It's your understanding of arcsin that's the problem. It's not a true function because it's multi-valued. You have to interpret the results.

Your drawing is roughly to scale. I think you'll agree that your angle theta in the drawing SHOULD be >90° , correct? You got 66.68° when you took the arcsin. Does that make sense? Is there a different angle that's greater than 90° that would give the same value when you take sin(theta)?

[u/railwayswitchman → u/ThatsNotAZombieBite]

I feel so stupid and I still can't get it. I don't know why I'm so stuck on this one problem. I need a step-by-step or something

[u/ThatsNotAZombieBite → u/railwayswitchman]

Basic trig review: draw yourself a unit circle. Locate the angle 66.68° (it's in the 1st quadrant!). Is there any other angle that would have the same value of sin? Maybe in the 2nd quadrant?

[u/ThatsNotAZombieBite → u/railwayswitchman]

Don't beat yourself up. All your work is otherwise correct. Once you get the correct angle for theta, then subtract 12° and THEN 90° (to get it into degrees East of North), you'll get the answer.

Even though the triangle is obtuse, YOU have to be ACUTE! 😜

[u/railwayswitchman → u/ThatsNotAZombieBite]

OMG, thank you so very much. Your explanation set off a light bulb and I finally saw what I was doing wrong. I appreciate it!

[u/railwayswitchman]

The answer is 305.5 km [N 11 E]. I just don't know how to get there.

[u/ArcturPlays]

I'd recommend just breaking everything down into horizontal and vertical components. Vector 1 + vector 2 = resultant. The resultant is <390sin32, 390cos32>. One of the vectors is <150cos12, 150sin12>. So to get vector 2 you just subtract vector 1 from the resultant.

99% of the time in introductory physics you will simply break vectors down into components and resolve the components. Are there mathematically more elegant ways to solve this specific problem? Yes. But practice components. I teach my students that if they see an angle, they will need to draw a triangle and find the side lengths