anne runs in a straight line for 1200 metres on a bearing of 39 then turns and runs in a straigh

1. First, we need to find the coordinates of Anne's starting point, let's call it A. We can assu

Anne runs in a straight line for 1200 metres on a bearing of...

Anne runs in a straight line for 1200 meters on a bearing of 39°, then turns and runs in a straight line for 2500 meters on a bearing of 146°. If she wishes to return to her starting point by running in a straight line, in which direction should she run (state as a bearing to the nearest degree)? Solution: To return to her starting point, Anne should run on a bearing of ?? degrees, to the nearest degree.

Transcript

00:01 Alright, so bearing was fun.

00:02 I looked up the definition of bearing which is a measurement of a clockwise turn off of north so if we are heading at a 39 degree bearing let me put it down here.

00:19 That means it is moving this way with this being 39 degrees and then she goes with a hundred and forty six bearing so that means she's going this way and this is one hundred and forty six and then we have this alright, so then i'm thinking law of sines and cosines which is what happened it's like okay, but where are the angles and stuff? um, obviously we know the sides, you know, this is 1200 and this one is 2500 now if we could only get some angles inside the triangle not the straightest lines ever but there we go we can drop the horizontal and vertical if that's 39 and that's 90 degrees because of horizontal and vertical.

01:09 This is 51 if this is 146 and if i take 90 away i'm gonna have to erase my 146 to get some room there if i take my 90 away from 146 i have 156 and of course, this is a straight line, which is 180 so 180 minus the 51 and the 56 gave me an angle of 73 yay, now i have an angle that's between the two sides.

01:43 So i have to use the law of cosines so x squared is equal to 1200 squared plus 2500 squared minus 2 times 1200 squared times 2500 squared times the cosine of 73 so you can type all that in you'll get let's see here do you get five million nine hundred and thirty five thousand seven hundred and seventy? million nine hundred and thirty five thousand seven hundred and seventy that is x squared.

02:22 So take the square root and x is 2436 not what we're asked for but it's what i could get.

02:33 So that's what i did so that's that's how i do better in math than most people because i don't go for what is the answer you're like, oh my gosh, i have to get an angle.

02:44 Why is she bothering to do this? i just take what they give me and run with it and i'm like, well that isn't what i needed so i must continue.

02:53 Okay, so i want the bearing down here still he is going not this way.

03:00 He is going this way, by the way alright, so we need that bearing one.

03:05 We need some angles down there.

03:07 Oh, yeah, we need some angles down there maybe if i get this angle somehow be able to get the angle i want i don't know but we'll see because i can get that angle because the law of sines now so the sine angle on top...

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