CPM Homework Help : PC3 Problem 11-157

What is the angle between two forces of $23$ N and $90$ N if the resultant force is $107$ N?

Hint:

Let the $23$ N force point directly to the right. Let the $90$ N force point in the direction $θ$ .
Express each force as a vector, sum the vectors, then write an expression for the magnitude of this resultant force.

Step 1:

$F_1+F_2=⟨23 + 90 \cos(\theta), 90 \sin(\theta)⟩$

Step 2:

$||F_1+F_2||=107$