What is the Solution to a Tension Problem using Trigonometry?

[jonnyboy]

Homework Statement

Two cables are attached to a sign at point A to steady the sign as it is being lowered. Using Trigonometry, determine a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied at A is vertical, b) the corresponding magnitude of R

Homework Equations

Use Law of cosines (R^2 = Q^2 + P^2 - 2QPcos(theta))
and Law of sines P/sin(opp. angle) = Q/sin(opp. angle)

The Attempt at a Solution

diagram is shown in attachment. I only have one magnitude and one angle and I'm supposed to get an angle alpha so that P is the min.

 

[Oerg]

I have no idea where ure stuck at but ill drop a small hint:

The horizontal component of force Q must cancel for the resultant to be vertical.

 

[jonnyboy]

Right, thanks. it's the small things that get me. taking the horz component of Q (80sin(35) = P = 45.9) gives the magnitude of p. Then, using law of sines to get alpha, I can get the third angle and then use law of cosines to get mag of R

 

[Oerg]

Right, thanks. it's the small things that get me. taking the horz component of Q (80sin(35) = P = 45.9) gives the magnitude of p. Then, using law of sines to get alpha, I can get the third angle and then use law of cosines to get mag of R

if you have already noticed if you went ahead with the above, alpha should be a right angle since the smallest force you need with p is a horizontal force to cancel out with the horizontal component of Q.