The resultant of two forces is 50N. If the forces are perpendicular to each other and one of them makes an angle 0f 30o with the resultant, find its magnitude.

Analyze the question: Two perpendicular forces have a resultant of 50 N. One force makes 30° with the resultant. We need "its" magnitude, meaning the force that makes the 30° angle.

Concept: When two forces are perpendicular, they form the sides of a right-angled triangle (or rectangle), and the resultant is the hypotenuse. A force making angle θ with the resultant is the adjacent side, so:

F₁ = R cos θ

The other force is F₂ = R sin θ.

Solution:

• R = 50 N, θ = 30°
• Force making 30° with the resultant: F₁ = 50 cos 30° = 50 × 0.866 = 43.3 N
• The other force: F₂ = 50 sin 30° = 25 N (this is option D, a distractor)

Check: √(43.3² + 25²) = √(1874.9 + 625) = √2500 = 50 N ✓

Answer: The force that makes 30° with the resultant is 43.3 N, which is option C.

Tip: The force adjacent to the angle uses cosine, and the force opposite uses sine. Read carefully which force the question asks for. Here, "its" refers to the force at 30°, so use cos 30°. Option D (25 N) is the trap for students who use sine.