Question

A particle undergoes two displacements. The first has a

Answer 1

First you need to draw the picture of the problem to better understand it. Like the one bellow. 

In this task you have 2 sides of triangle and we can calculate angle between them. Angle between them is 120 - 35 = 85 degrees.

Once you have those 3 variables you can calculate third side of triangle using cosine law.
a - second displacement
b - first displacement
c- resultant displacement.

$a^{2} = b^{2}+ c^{2}-2*b*c*cos85$
now we just need to calculate this.
$a^{2} = 38439.458$
a = 196

now, we use cosine law again to find the angle between second and first displacement.
$\alpha = 45.36$ degrees

The angle marked with "?" in the graph is our direction angle. We will call it $\beta$

$\beta =90-30-45.36 = 14.64$

Second displacement has magnitude of 196 and a direction of -14.64 with positive x axis