Answer
See work. The forces must be added as vectors. The magnitude of the resultant force is less than the sum of the magnitudes of the individual forces, and depends on the angle between them.
Work Step by Step
Choose a coordinate system where the positive x axis is in the direction of the force applied by Rover.
Find the x-components of the 2 forces.
$F_{Rover,x}=270 N cos 0^{\circ}$
$F_{Fido,x}=300 N cos 60^{\circ}$
Add them to find the x-component of the sum.
$F_{sum,x}=270 N cos 0^{\circ} + 300 N cos 60^{\circ}=420N$
Find the y-components of the 2 forces.
$F_{Rover,y}=270 N sin 0^{\circ}$
$F_{Fido,y}=300 N sin 60^{\circ}$
Add them to find the y-component of the sum.
$F_{sum,y}=270 N sin 0^{\circ} + 300 N sin 60^{\circ}=260N$
Find the resultant force magnitude by using the Pythagorean Theorem.
$F=\sqrt{420^2+260^2}N=494N$
Find the resultant force’s angle by using trigonometry.
$\theta=tan^{-1}(\frac{259.8N}{420.0N})=31.7^{\circ}$
