1. A party of hikers walks 8 km from camp on 30 degrees, then turns and walks 6 km on course 160 degrees. Find the magnitude of the net displacement from camp.

2. A ship leaves port A and sails 61.1 km course 131 degrees 50' to point B. Then it sails 76.5 km on course 36 degrees 30' to point C. Find the bearing of point C from point A.

note 160 = south - 20

North distance = 8 cos 30 - 6 cos 20
East distance = 8 sin 20 + 6 sin 20

distance = sqrt (North^2 + east^2)

2.
call it 132 = south - 48
north distance=-61.1cos 48 +76.5sin 36.5
east distance =61.1sin48 +76.5cos 36.5
tan theta = north/east

1. I sketched a triangle, and noticed I could use the cosine law:

R^2 = 8^2 + 6^2 - 2(8)(6)cos 50°
= 38.2923...
R = appr 6.189 km

or

use vectors
first vector = (8cos30 , 8 sin 30) = (6.9282 , 4)
2nd vector = (6cos160, 6sin 160) = (-5.63815.. , 2.05212)

sum = ( 1.29004.... , 6.05212)

magnitude = √( 1.29004..^2 + 5.05212^2)
= appr 6.189

Do the 2nd in the same way.

LOL, physicist / mathematician again.

To find the magnitude of the net displacement from camp, we can use vector addition.

1. Convert the given distances and directions into vector components:
a) The first leg of the journey is 8 km on a 30-degree course. This can be broken down into horizontal and vertical components using trigonometry:
- Horizontal component = 8 km * cos(30°)
- Vertical component = 8 km * sin(30°)
b) The second leg of the journey is 6 km on a 160-degree course. Again, use trigonometry to find the components:
- Horizontal component = 6 km * cos(160°)
- Vertical component = 6 km * sin(160°)

2. Add the horizontal components together and the vertical components together to get a single resultant vector.
- Resultant horizontal component = horizontal component of leg 1 + horizontal component of leg 2
- Resultant vertical component = vertical component of leg 1 + vertical component of leg 2

3. Use the Pythagorean theorem to find the magnitude of the net displacement vector from the camp:
- Magnitude = sqrt((Resultant horizontal component)^2 + (Resultant vertical component)^2)

Now, let's solve the second question:

To find the bearing of point C from point A, we can use trigonometry and vector analysis.

1. Convert the given distances and directions into vector components:
a) The first leg of the journey is 61.1 km on a 131 degrees 50' course. This can be broken down into horizontal and vertical components:
- Horizontal component = 61.1 km * cos(131 degrees 50')
- Vertical component = 61.1 km * sin(131 degrees 50')
b) The second leg of the journey is 76.5 km on a 36 degrees 30' course. Again, use trigonometry to find the components:
- Horizontal component = 76.5 km * cos(36 degrees 30')
- Vertical component = 76.5 km * sin(36 degrees 30')

2. Add the horizontal components together and the vertical components together to get a resultant vector.
- Resultant horizontal component = horizontal component of leg 1 + horizontal component of leg 2
- Resultant vertical component = vertical component of leg 1 + vertical component of leg 2

3. To find the bearing of point C from point A, we can use the tangent function:
- Bearing = arctan((Resultant vertical component) / (Resultant horizontal component))

Note: Don't forget to convert the resulting angle from radians to degrees if necessary.