Find the angle between the forces given the magnitude of their resultant?

Question

Force 1 = 45 pounds
Force 2 = 60 pounds
Resultant force = 90 pounds

(hint: write force 1 as a vector in the direction of the positive x-axis and force 2 as a vector at an angle theta with the positive x-axis) <--(what the book suggested...)

Answer 1

F1= 45 i
F2= 60 cos t*i+60 sin t *j
F1+F2 = (45+60cos t) i+60 sin t j

(45+60 cos t)^2 +(60 sin t) ^2 = 8100
2025 +3600 cos^2t +5400 cos t +3600 sin^t =8100
5625 +5400cost = 8100
cos t=0.4583 so t=62.72 º

Answer 2

i) Let Force-1 be P; Force-2 be Q and Resultant be R and let the angle between P & Q be u. If P & Q are represented by the adjacent side of parallelogram, then R is represented by the diagonal of the parallelogram. ii) BY Parallelogram law of forces, R is given by: R² = P² + Q² + 2*P*Q*cos(u) So, cos(u) = (R² - P² - Q²)/(2*P*Q) iii) Substituting the given values and solving cos(u) = 11/24 So u = 62° 41'

Answer 3

Oh fun! but i don't time now, (halloween party to goto...) but If no ones answers before I'm back, I'll do it!