An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. he was supposed to travel due north for 5.3 km, but when the snow clears, he discovers that he actually traveled 8.5 km at 54o north of due east. (a) how far and (b) in what direction (south of due west) must he now travel to reach base camp?

(a) He must travel 5.25 km

(b) 17.7° south of west

Step-by-step explanation:

(Please see attached file)

1. He was supposed to travel 5.3 km due north to return to base camp

(vector S)

S = (Sx, Sy)

Sx= 0

Sy= 5.3

2. He discovers that he actually traveled 8.5 km at 54° north of due east (vector D)

D= (Dx, Dy)

Dx= Dcos Ф = 8.5cos54° = 5.0

Dy= Dsen Ф = 8.5sen54° = 6.9

3. He now needs to reach the base camp. Then, we need to find vector R.

From vectors addition/subtraction:

S = D + R

R = S - D

R= (Rx, Ry)

Rx = Dx - Sx = 0 - 5.0 = -5.0

Ry = Dy - Sy = 5.3 - 6.9 = -1.6

Magnitude of R =

Magnitude of R =

Magnitude of R = 5.25 km

Direction:

tanβ =

tanβ =

tanβ = 0.32

β = tan-1 (0.32)

β= 17.7° south of west

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?