# Tutor.com Trigonometric Functions Session

##### May. 20, 2012

Session Transcript - Math - Trigonometry, 5/12/2012 10:18PM - Tutor.comSession Date: 5/12/2012 10:18PM
Length: 42.7 minute(s)
Subject: Math - Trigonometry

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)
[00:00:03] A plane flies 500 kilometers with a bearing of N 44 W from Naples to Elgin (see figure). The plane then flies 720 kilometers from Elgin to Canton. Find the bearing of the flight from Elgin to Canton (BE CAREFUL!) (APPROX)

Rodney W (Tutor)
[00:00:10] hi
[00:00:21] are you studying vectors?
[00:02:21] Canto and Naples at same longitude?

Guest (Customer)
[00:03:00] Hello before we start I have to say.
[00:03:33] Iam in algebra 2 and we are doing the last chapter but it is trigonometry.

Rodney W (Tutor)
[00:04:08] no problem

Guest (Customer)
[00:04:07] My teacher created this question to see who can solve it so I apologize if this looks confusing but its because it is original.
[00:04:19] Its a trick question (extra credit)

Rodney W (Tutor)
[00:04:40] is Canto due west of Naples?
[00:05:44] Is there a west line on the diagram?

Guest (Customer)
[00:05:44] Im not aur ebecause this is how it is drawn on my Hw.
[00:05:53] but there is no wes line

Rodney W (Tutor)
[00:06:04] ok
[00:06:19] have you studied law of sines?

Guest (Customer)
[00:06:44] yes SinA / a = SinB / b = SinC / c

Rodney W (Tutor)
[00:06:53] OK
[00:07:12] the problem is this
[00:07:33] unles we know the direction of Canton from Naples
[00:07:47] this is going to be difficult,
[00:07:54] if not unsolvable
[00:08:15] you have no other information in the problem?

Guest (Customer)
[00:08:35] well this is all the information i was given
[00:08:49] my teacher said thi will be difficult.

Rodney W (Tutor)
[00:09:19] does it LOOK like Canto is west of Naples on your diagram?

Guest (Customer)
[00:10:11] yes its exactly how i drew it on here and if we are starting from naples going left is WEST which is Canton

Rodney W (Tutor)
[00:10:24] OK
[00:10:49] we will assume Canton is due west of Naples for this solution
[00:11:09] this gives us a triangle to work with

Guest (Customer)
[00:11:13] it is ( ;

Rodney W (Tutor)
[00:11:19] where now we know an angle
[00:12:08] the bearing Naples to Elgin was N44W

Guest (Customer)
[00:12:09] how did you find 46?

Rodney W (Tutor)
[00:12:41] If Canton is west of Naples 44+46=90
[00:12:58] the angle between N and W

Guest (Customer)
[00:13:03] oh i see ( :

Rodney W (Tutor)
[00:14:04] now we can do the angle I marked x using law of sines
[00:14:13] OK?

Guest (Customer)
[00:14:25] yes we can want me to set it up? ( :

Rodney W (Tutor)
[00:17:46] what you get for the angle?

Guest (Customer)
[00:18:53] 29.96967237

Rodney W (Tutor)
[00:19:01] great!
[00:19:05] approx 30
[00:19:26] draw a north-south line through Elgin

Guest (Customer)
[00:19:42] just a sec ( :
[00:21:18] hello?

Rodney W (Tutor)
[00:21:30] I'm here
[00:21:41] you wanted a sec

Guest (Customer)
[00:21:55] oh ok well im ready ( :

Rodney W (Tutor)
[00:22:11] N-S line through Elgin
[00:23:00] see?
[00:23:20] assuming the Canto-Naples line is E-W
[00:23:35] we construct the right triangle
[00:23:55] what is the angle I labeled B?
[00:24:24] you here?

Guest (Customer)
[00:24:25] yes correct
[00:24:40] sorry i was trying to comprehend everything

Rodney W (Tutor)
[00:24:52] ok
[00:24:59] can you tell me B?

Guest (Customer)
[00:25:18] yes im sure i can

Rodney W (Tutor)
[00:25:27] it is?
[00:26:21] B=60
[00:26:24] OK?

Guest (Customer)
[00:26:25] 60

Rodney W (Tutor)
[00:26:38] that line is N-S

Guest (Customer)
[00:26:54] yes correct

Rodney W (Tutor)
[00:26:56] so what is the bearing from Elgin to Canton?

Guest (Customer)
[00:27:30] im not sure

Rodney W (Tutor)
[00:27:53] its 60 degrees west of south
[00:28:00] S60W
[00:28:23] is how they put it if we follow the format of your problem
[00:28:38] understand?

Guest (Customer)
[00:28:46] oh ok i wasnt sure what you ment

Rodney W (Tutor)
[00:29:26] this solution is based on the assumption that Canton and Naples lie on an East-West line
[00:29:40] if that's not true
[00:29:48] the whole thing is off
[00:30:05] but there would be no way to solve the problem either

Guest (Customer)
[00:30:24] ok well than what is N-s?

Rodney W (Tutor)
[00:30:40] north-south

Guest (Customer)
[00:30:54] but what number gos in between?

Rodney W (Tutor)
[00:31:07] in between what?

Guest (Customer)
[00:31:28] N - S ? just like N 44 W

Rodney W (Tutor)
[00:31:52] the answer is S 60 W
[00:32:23] you are measuring bearings from North or South
[00:32:39] so so many degrees to the East or West

Guest (Customer)
[00:32:44] oh so that is my answer S 60 W?

Rodney W (Tutor)
[00:32:51] YES
[00:32:59] do you understand??

Guest (Customer)
[00:33:29] yes kind of

Rodney W (Tutor)
[00:34:19] let me draw this on a rectangular coordnate sytem

Guest (Customer)

Rodney W (Tutor)
[00:36:55] a simple triangle problem
[00:37:20] we used law of sines to find angle at Canton to be 30 degrees

Guest (Customer)
[00:37:29] yes

Rodney W (Tutor)
[00:38:04] we drew a vertical line through Elgin
[00:38:16] constructing a right triangle

Guest (Customer)
[00:38:19] which was the N-S line correct?

Rodney W (Tutor)
[00:38:25] yes
[00:39:20] we found the angle between the North-South line and the direction from Elgin to Canton to be 60 degrees
[00:40:04] setting up a beaqring compass at Elgin
[00:40:26] we see that Canton bears S 60 W from Elgin
[00:40:40] understand?

Guest (Customer)
[00:41:19] ahh yes makes perfect sense now! ( : sorry if i wasted much of your time on this session. I do apologize.

Rodney W (Tutor)
[00:41:31] no problem
[00:41:44] answer without understanding is pointless

Guest (Customer)
[00:41:53] you've been a great help.

Rodney W (Tutor)
[00:42:00] we done?