Question

A spelunker is surveying a cave. She follows a passage 140 m straight west, then 250 m in a direction 45∘ east of south, and then 280 m at 30∘ east of north. After a fourth unmeasured displacement, she finds herself back where she started.

for the last displacement x=188.61 and y = 20.39 therefore the vector is a straight 190m line with an angle of ?

Answer 1

measured from the positive x-axis,
tanθ = y/x = 20.39/188.61
so, θ = 6.17°

That's E 6.17° N
or, as a course heading, 83.83°

Answer 2

total east = -140 + 250 sin 45 + 280 sin 30 = 176.78

total north = 0 -250 cos 45 +280 cos 30 = 65.71

I do not understand where you get that last x and y

in my opinion you must go west 176.78 and south 65.71

tan^-1 65.71/176.78 = 20.4 deg south of west

Answer 3

i got confused while in a part but i already checked it was 20.4 deg