Solve Crane Tension: 2 Cable Equations & Triangle Angles

[juggalomike]

Homework Statement

A crane is used to lift a concrete pipe weighing 5kN into place.

Homework Equations

The Attempt at a Solution

The picture is in my book, but i am certain my problem is in my algebra(i have the layout correct)

T_ac*cos(20)=T_ab*sin(3.58) X direction
5+T_ac*sin(20)=T_ab*cos(3.58) Y direction

I am for some reason drawing a blank when it comes to how i can work this out, i tried solving for T_ac in equation 1 then plugging that into equation 2 but then i am running into an algebraic nightmare. One other problem aswell(its part of the question)

I am given a triangle where Hypotenuse=4m and opposite=.25m, so using A^2+b^2=c^2 i got 3.99 for b. Then i used theta=arccos(adjacent/hypotenuse)=4.05, but for theta=arcsin(opposite/hypotenuse)=3.58. What am i doing wrong?

 

[rock.freak667]

The Attempt at a Solution

The picture is in my book, but i am certain my problem is in my algebra(i have the layout correct)

T_ac*cos(20)=T_ab*sin(3.58) X direction
5+T_ac*sin(20)=T_ab*cos(3.58) Y direction

Since you didn't post a picture of the FBD, I will have to assume it is how I am expecting it to look.

The equation for the x-direction should be

T_accos(20)=T_abcos(3.58)

and for y-direction

5=T_acsin(20)+T_abcos(3.58)

in which you'd just solve simultaneously.