What is the magnitude and resulting angles

Question

Forces of 15 and 24 kg act on a point at an angle of 62 Degrees with respect to each other. Find the magnitude of the resulting force and the angles the resultant force makes with the given forces.

Answer 1

If we are looking for the resultant force of two given forces with given angle between them, we can use the Law of Cosine and then Law of Sine for the other angles and direction.

c² = a² + b² - 2ab • cos(θ)

Where c is the resultant force

a and b = two given forces = 15 and 24 kg.

θ = 180º minus the angle between two given forces = 180 - 62 = 118°

c² = (15)² + (24)² - 2(15)(24) • cos(118°)

c² ≈1139.02

c ≈ 33.75 kg.

For the angle:

Where:

β = angle between c (the resultant vector) and 15 kg.

α = angle between c (the resultant vector) and 24 kg.

sin (θ) / c = sin (β) / 24

sin (β) = 24 sin (θ) / c = 24 sin (118°) / 33.75

sin (β) = .6279

β = 38.89°

α = 62° - 38.89°

α = 23.11°