Geometry and Trigonometry HELP!!

[seretide]

Hey guys!

i have been trying to work these out for the past hour and can't seem to get it right, or even near it. Can anyone please help me with these? I know it is quite a bit, but any help is very much appreciated.

Thanks!

1. Joan walks north-east from her camp at the point A for 10km to the point B. She then turns 50 degrees clockwise and walks a further 10km until she reaches point C.

a. Find the true bearing on which Joan walks from B to C.
b. Calculate the distance from A to C.
c. Find the true bearing of C to A.
d. If Joan walks at 5km/hr, calculate the time she would have saved by walking directly from A to C 
    rather than travelling from A to C via B.

2. Adam and Jean are at pints A and J respectively. Adam is at height 100m above sea level, while Jean is 400m above sea level. On a map, horizontal distances between points with a scale of 1:100000, the distance between their locations if 5cm. Adam is tired to walk so Jean walks in a direct line to Adam.

a. Find horizontal distance between Adam and Jean initially. Answer in km.
b. Find distance Jean needs to walk to reach Adam. Answer in km.
c. Find average slope of the direct path from Adam to Jean.

[brightsky]

1. a) 270 - 45 - 50 = 175 T.
b) using cosine rule, AC = sqrt(10^2 + 10^2 - 2*10*10*cos(50)). simplify accordingly.
c) so going the long way, she would have taken 20/5 = 4 hrs. going directly from A to C, she would've used sqrt(10^2 + 10^2 - 2*10*10*cos(50))/5 hrs. so the time she saved is 4 - sqrt(10^2 + 10^2 - 2*10*10*cos(50))/5, whatever that may be on the calc.

2. incredibly vague question, but i'll try my best:
a) i'm assuming this means that you disregard any altitude difference in their respective locations. so if the distance between their locations on the map is 5 cm, then the real distance 5000 m [this is the hypotenuse]. so the horizontal distance between them would be sqrt(5000^2 - 300^2) m. convert it to km accordingly.
b) i'm assuming that's 5000 m??
c) slope would be 300/ sqrt(5000^2 - 300^2). evaluate with calc.

[seretide]

Thank you for the quick response! Can you please explain a though for question 1?

[MasterEds]

1. Ok, what you gotta do first for 'a' is to draw it out (Very important) with a compass rose at each point (so point A, B & C).
2. From here, we know NE is 45T, so draw a line NE labelled 10km.
3. At the end of the line, label point 'B' AND draw a compass rose.
4. imagine she is still facing 45T from point 'A.' Which means A is 225T from point 'B'
5. then we get 225T - 50 degrees cause she turns around 50 degrees.
6. Result is 175T