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, included free with weekly lessons.

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.

Ready to master it?

Jump into unlimited practice. Your Winny Score tracks you to 100. And if it won't click, a real tutor will make it click: first lesson free.

Start practicing