Resultant displacement and angle

[bearhug]

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 69.7 m north, 246.8 m east,127.4 m at an angle 37.8 (degrees) north of east, and 127.4 m south. What is the resultant displacement from the cave enterance? The angle should be positive between 0 and 360.

I drew a diagram not 100% accurate but enough to give me a picture. And the resultant displacement I took to be the distance from point A to point D (start point to end point). The equations I used are as follows:
ax= 69.7 cos(90) ay= 69.7 sin(90) = 0, 69.7
bx= 246.8 cos (0) by= 246.8 sin (0) = 246.8, 0
cx= 127.4 cos(37.8) cy= 127.4 sin(37.8) = 100.7, 78.1
dx= 127.4 cos(90) dy= 127.4 sin(90) = 0, 127.4

I found Rx = 347.5
Ry = 275.2

R = (347.5^2 + 275.2^2)^1/2
= 443.2m to be the resultant displacement

angle = tan= 275.2/347.5= 38.4 degrees

Is this the right method?

 

[Doc Al]

The equations I used are as follows:
ax= 69.7 cos(90) ay= 69.7 sin(90) = 0, 69.7
bx= 246.8 cos (0) by= 246.8 sin (0) = 246.8, 0
cx= 127.4 cos(37.8) cy= 127.4 sin(37.8) = 100.7, 78.1
dx= 127.4 cos(90) dy= 127.4 sin(90) = 0, 127.4

Rewrite that last equation. If "north" is at an angle of 90 degrees, then south must be directly opposite, which is 270 degrees (or -90 degrees).

(Other than that error, your method looks just fine.)

 

[kyle8921]

I cannot confirm if your method is correct without knowing the specific context and assumptions of your diagram and equations. However, in general, the resultant displacement can be calculated by adding the individual displacements using vector addition. This involves breaking down each displacement into its vertical and horizontal components, adding them separately, and then using the Pythagorean theorem to find the magnitude of the resultant displacement. The angle can then be calculated using trigonometric functions.