Two ship P and Q left a port R at the same time.Q sailed on a bearing of 150 while P sailed on the north side of Q.After a distance of 8km and 10km by P and Q respectively,their dirtance part was 12km.find the bearing of P from R.

Answer 1

You sail on a HEADING, not a bearing.
You take a compass bearing on something else as in P from R

Q:
sailed on a heading of 150
which is 30 degrees east of south
(draw that)

we will use the law of cosines
RQ = 10
RP = 8
QP = 12
we want first the angle call it x opposite QP
QP^2 = RQ^2 + RP^2 - 2 QP cos x
144 = 100 + 64 - 24 cos x
cos x = 20/24
x = 33.6 degrees
so the total angle from the south direction east to RP is 30+33.6
= 63.6 east of south
on a compass that bearing is
180 - 63.6 = 116.4 or around ESE

Answer 2

It is not correct

Answer 3

12^2=8^2+10^2-2*8*10cosR
144=64+100-160cosR
144-164=-160cosR
-24/-160=cosR
0.125=cosR
R=cos^-1(0.125)
R= 82.8
The bearing of P from R is 180-30-82.8=67.2
N67E or 067

Answer 4

SinR/r=sinQ/q
=sinR/12=sin30/10
cross multiply
10sinR=12sin30
sinR=12sin30/10
R=36.9 or 37
P=R+Q
P=30+37
P=67

Answer 5

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Answer 6

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