Engineering Statics - Hibbeler?

Question

Hibbeler Statics - Edition 11 Problem 2-48.

Basically, three forces acting on a bracket. Two of the forces along with their direction are known but the third is unknown. The resultant force of all three must be 800N and at 30 degrees above the positive x axis.

I have got it down to this and I know it's correct so far but I don't know where to go from here.....

Resultant Force X =

F1cosθ = 800sin60 - 166.15

F1cosθ = 526.67

Resultant force Y =

F1sinθ = 200 + 69.23 + 800cos60

F1sinθ = 669.23

Any help is much appreciated...cheers :-)

Answer 1

You should be able to solve this via solving the two simultaneous equations:

F1 = 526.67/cosθ

(526.67/cosθ) sinθ = 669.23

tanθ = 1.271

θ = 51.8 deg

F1 = 526.67/cos(51.8) = 851.65 N