A bearing question which I dont know...Please helpppp,10 points,Please...I need ur help?

Question

A ship sails directly from a port P to a point Q. Which is 15km due east of a lighthouse L.
Given that angle PLQ=65 degrees and angle PQL=35 degrees
a) Calculate
i) the bearing of P from L
ii) the bearing of L from P
iii) the bearing of P from Q
b) Find the shortest distance between the lighthouse and the ship during its journey

Answer 1

This question does not have a unique answer.
Point P could be either North or South of the line between L and Q.

So you have two cases to consider.

Draw a diagram and mark in all angles to see the two cases.

If P is North of QL
i) the bearing of P from L

E 65 deg N
or N 25 deg E
or 025 deg True

ii) the bearing of L from P

To get the back bearing from P to L- add 180 deg to the bearing from L to P

205 deg True
or South 25 deg West


iii) the bearing of P from Q

West 35 deg North
or 305 deg True

b) Find the shortest distance between the lighthouse and the ship during its journey.

The shortest distance will be when the ship is at P
To find the distance PL use the Sine Rule

PL / sin 35 = 15 / sin 80
PL = 15 sin 35/sin 80
PL = 8.74 km

This answer will be the same for both cases P North or South of QL.

Answer 2

This question does not have a unique answer. It has two, depending on whether P is north or south of L.

Let's use
P if north of L
P' if south of L

a) Calculate
i) the bearing of P from L
LP = 90 - 65 = 25°
LP' = 180 - 25 = 155°

ii) the bearing of L from P
PL = 25 + 180 = 205°
P'L = 155 + 180 = 335°

iii) the bearing of P from Q
QP = 360 - (90 - 35) = 360 - 55 = 305°
QP' = 180 + (90 - 35) = 180 + 55 = 235°

b) Find the shortest distance between the lighthouse and the ship during its journey.

The shortest distance is when the ship is at P or P'. The distance is the same for either location. Use the Law of Sines.

LP / sin( LP / sin(35°) = 15 / sin(25° + 55°) = 15 / sin(80°)
LP = 15 [sin(35°) / sin(80°)] ≈ 8.7363717 km

Answer 3

he bearing of P from L = 180 - angle PLQ
= 180 - 65
= 115 degrees.

Similarly
the bearing of L from P
= angle 180 - 115
= 65 degrees.

Bearing of P from Q
= 180 - angle PQL
= 180 - 35
= 145 degrees.

the shortest distance between the lighthouse and the ship during its journey
This is slightly tough.
Draw perpendicular from L to PQ
Its length is shortest distance

you will need some geometric calculations here. Using pythogoros theorem.

start by assuming length as h. Use sin/cos/tan and then add lengths to get distance PQ in terms of h

I know you can solve now.

Thank you.

Answer 4

just a guess. the shortest distance between the lighthouse and the ship.would be when the ship makes port. or from q to l