Math for College Technology (MCT4C) · Trigonometric Functions

Resultant of two force vectors

Use the law of cosines (R^2 = F1^2 + F2^2 + 2F1F2*cos(theta)) to find the magnitude of the resultant of two force vectors. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCT4C-TF1

Try one

Two hydraulic rams push against a jig with forces of 39 N and 28 N, at an angle of 36deg between their directions of pull. Find the magnitude of the resultant force, to one decimal place.

R = √(F1² + F2² + 2·F1·F2·cos(theta))

Answer: 63.8

See one solved, step by step

Two ropes are used to winch an ATV out of a ditch with forces of 67 N and 57 N, at an angle of 65deg between their directions of pull. Find the magnitude of the resultant force, to one decimal place.

R = √(F1² + F2² + 2·F1·F2·cos(theta))

📘 Worked solution

1R = √(F1² + F2² + 2·F1·F2·cos(theta))For two vectors with an angle theta between them, this gives the magnitude of their sum (the resultant).

2R = √(67² + 57² + 2(67)(57)cos(65deg))Substitute the two force magnitudes and the angle between them.

3= √(7738 + 3228) = √(10966)Evaluate the cosine and combine the terms under the root.

4= 104.7 NTake the square root to find the magnitude of the resultant force.

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