A particle undergoes two displacements, measured

Question

from the positive x-axis, with counterclockwise
positive. The first has a magnitude
of 11 m and makes an angle of 67 ◦ with the
positive x axis. The resultant displacement
has a magnitude of 7.7 m directed at an angle
of 98 ◦
from the positive x axis.

Find the angle of the second displacement
(measured from the positive x axis, with counterclockwise
positive and within the limits of
−180◦
to +180◦
).
Answer in units of ◦

Answer 1

you want (x,y) such that

(11cos67,11sin67) + (x,y) = (7.7cos98,7.7sin98)

Evaluate x and y, and then find θ such that tanθ = y/x

Answer 2

x-comp -5.3696
y-comp -2.5
magnitude 5.92
angle 335 degrees