### Home > PC3 > Chapter 11 > Lesson 11.2.5 > Problem11-157

11-157.

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

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.

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

$||F_1+F_2||=107$