Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Question

anonymous · Answer

i'm really confused could someone help me i haven't done this before so i don't know how it works.

anonymous · Answer

Use the cosine rule. do you know it?

anonymous · Answer

yes but im not sure how to apply it

anonymous · Answer

first how do you get the direction?

nurali · Answer

F = 150 (cos(30), sin(30)) + 75 (cos(150), sin(150)) 
F = 150 (√3/2, 1/2) + 100 (-√3/2, 1/2) 
F = (75√3−50√3, 75+50) 

Magnitude of resultant force 
= √((75√3−50√3)² + (75+50)²) 
= 50√7 
≈ 132.287 pounds 

Direction of resultant force 
= tan⁻¹((75+50)/(75√3−50√3)) 
≈ 70.89°

nurali · Answer

Welcome to Openstudy.

anonymous · Answer

thx! that helps so much:) i was on track with about the first step but i didn't know what to do after.

nurali · Answer

My Pleasure.