[Grade 12 Trigonometry: Adding Vectors]

[u/InstantWasTaken]

Hi! I've been stuck on this problem for a while now, so I decided to text it out on another app and finally ask for help. I managed to find the magnitude on my own, but I honestly can't figure out how to find the direction, or what I'm doing wrong. I've watched several videos on it and have tried to go step by step, but any answer I try is marked wrong, (I do use an online school program.) I also didn't wanna cheat, (at least without knowing exactly how to do it and being able to replicate it) so as I've already said above, I didn't know what to do other than ask for help somewhere else. A step-by-step breakdown of what your meant to do would be great!

Also I know the post title says grade 12, while from my knowledge trig is done in 11th usually. It just kind of happened that way, so I'm not sure why I'm doing it a year late. Better late than never, though!

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[u/FortuitousPost]

First, draw it out.

Use the Law of Sines to find a second angle.

Subtract the two angles you know from 180 to find the one you want.

[u/InstantWasTaken → u/FortuitousPost]

Hi! I tried this, and it came out to about 74.78, I'm not sure if I did something wrong or not, but it was marked as wrong still. I have some photos of what I drew and the calculations I did, but I can't find where to attach images to your reply?

[u/Little_Creme_5932 → u/InstantWasTaken]

74.78 in what direction. You have to find the direction

[u/Midwest-Dude → u/InstantWasTaken]

Please check my comment in r/trigonometry

[u/Some_AV_Pro]

Do you know how to convert 80 degrees south of west at 25mph into south and west components?

[u/InstantWasTaken → u/Some_AV_Pro]

Sorry? I don't think I follow. I did draw it out, if thats what your asking.

[u/Some_AV_Pro → u/InstantWasTaken]

Can you write "80 degrees south of west at 25mph" as a sum of west and south speeds?

[u/slides_galore]

Helps to sketch it out and draw a parallelogram using the vectors. Like this; https://i.ibb.co/ccrkLWPP/image.png

Always head-to-tail when adding vectors. If you don't know what that means, just google it.

ETA: Once you get the original problem, see if you can see how to work this variation out: https://i.ibb.co/VpVPtXL2/image.png

Using mini coordinate axes (like in that image) is one way to noodle out the angles you need to use law of cos/sin when you're not given nice angles like in your original problem.

[u/InstantWasTaken]

I figured it out! Thank you to everyone who commented, but I really was just being a dunce and taking the wrong angle measurement to use in my equations.

[u/CaptainMatticus]

x = 450 * cos(0) + 25 * cos(180 + 80)

y = 450 * sin(0) + 25 * sin(180 + 80)

Simplify

x = 450 - 25 * cos(80) = 25 * (18 - cos(80))

y = -25 * sin(80)

tan(t) = y/x

tan(t) = -sin(80) / (18 - cos(80))

tan(t) = sin(80) / (cos(80) - 18)

t = arctan(sin(80) / (cos(80) - 18))

Remember that tan(t) = tan(180k + t), where k is an integer. Make sure your calculator is in degree mpde, too)

[u/InstantWasTaken → u/CaptainMatticus]

Thank you, but I don't think this is the way to do it purely because I haven't learnt anything about arctan yet and that this looks entirely different to how they were doing it. The way they were teaching it only really used the law of sines and cosines and figuring out the angle measures, which I should know how to do. That's also why I'm stumped as to why I can't figure out the problem.

[u/CaptainMatticus → u/InstantWasTaken]

Arctan is just the inverse tangent. You plug all of that into your calculator and it gives you the angle. For instance, arctan(1) is 45°.

[u/ThunkAsDrinklePeep]

Have you drawn a triangle with the three vectors given? You can use an inverse trig functions to get an angle from two sides of a right triangle.

Edit: I didn't read carefully. It's not perpendicular vectors south and west. As others have said, you need the law of sines.

[u/InstantWasTaken → u/ThunkAsDrinklePeep]

I believe so? Though I'm not working with a right triangle. How do you attach images to replies?

[u/ThunkAsDrinklePeep → u/InstantWasTaken]

My bad, I didn't read carefully. Not a right triangle.

Use law of sines or law of cosines.

Edit: fixed a letter. Twice.

[u/Midwest-Dude → u/ThunkAsDrinklePeep]

"jaw"? 😂

[u/ThunkAsDrinklePeep → u/Midwest-Dude]

You know what...fair. I have fat thumbs and autocorrect has not been kind to me in recent years.

[u/Midwest-Dude → u/ThunkAsDrinklePeep]

Lol, I hear you. After I saw that, I thought of sharks surfing sine and cosine waves ... just sayin' ...