The magnitude of the resultant force is approximately 31.6977.
Here's how we can calculate it:
Step 1: Resolve the forces into horizontal and vertical components.
Horizontal component of 15 N force: 15 N * cos(60°) = 7.5 N
Vertical component of 15 N force: 15 N * sin(60°) = 12.99 N
Horizontal component of 20 N force: 20 N * cos(15°) = 18.48 N
Vertical component of 20 N force: 20 N * sin(15°) = 5.17 N
Step 2: Add the horizontal and vertical components separately.
Horizontal component: 7.5 N + 18.48 N = 25.98 N
Vertical component: 12.99 N + 5.17 N = 18.16 N
Step 3: Apply the Pythagorean theorem to find the resultant force.
Resultant force = √(Horizontal component^2 + Vertical component^2)
Resultant force = √(25.98 N^2 + 18.16 N^2)
Resultant force ≈ 31.6977 N or 31.68 N
Therefore, the magnitude of the resultant force is approximately 31.6977. This matches your answer, confirming that your calculation is correct.