bearings + trigonometry

[willow (she/her)]

hi i'm doing a question that combines bearings and sine/cosine rule. i'm so confused on how to work it out so help would be appreciated!!

P, Q and R are three points on a map.
Q is 47km and on a bearing of 055degrees from P.
R is 79km and on a bearing of 159degrees from Q
Calculate the distance between P and R rounded to 1 DP.

my main problem is i have no idea how to construct the triangle because i find bearings confusing.
my attempt (which is probably wrong)
159-55=104 which is the angle at Q in the triangle
so then using the cosine rule
a²=47²+79²-2 x 47 x 79 x cos(104)
a²=10246.512
and then square root to get a/ PR = 101.2km (1DP)

 

[Romsek]

Your answer is correct. Do you want any more help?

 

[willow (she/her)]

One thing to get squared away from the start is what sort of bearings are we talking about.

(Aero)Nautical bearings have 0 degrees due north and increase as you move clockwise through east, south, west.

Everyone else uses bearings that have 0 degrees due east and increase as you move counter clockwise through north, west, south.

When I hear the word "bearings" I usually think of Nautical bearings.

Hi so I think it's referring to Nautical bearings.

 

[Romsek]

Hi so I think it's referring to Nautical bearings.

You answered it correctly.