Answer
x-component: $(4580 m)(cos 122.4 ^{\circ}) = -2845 m$
y-component: $(4580 m)(sin 122.4 ^{\circ}) = 3589 m$
The z-component was given as 2450 m.
The magnitude of the displacement is $5190 m.$
Work Step by Step
The x component is negative and the y component is positive, because the summit is to the west of north. The angle of the displacement vector measured counterclockwise from the positive x axis is 122.4 degrees.
x-component:
$$(4580 m)(cos 122.4 ^{\circ}) = -2845 m$$
y-component:
$$(4580 m)(sin 122.4 ^{\circ}) = 3589 m$$
The z-component was given as 2450 m.
The magnitude of the displacement is obtained using the 3 components and the Pythagorean theorem, and is 5190 m.
