Question

A 150-N bird feeder is supported by three cables. Find the tension in each cable.

Answer 1

X axis : -t1 cos 60 + t2 cos 60 = 0
 
            t2 cos 60   = t1 cos 60    ; t2   = t1

Y axis : t1 sin 60  + t2 sin 60 - 150 = 0

since t2 = t1

2t1 sin 60 =  150

t1 ( sqrt(3)/2)  = 150/2

t1   = 50 [sqrt(3)]

t2 = 50 [sqrt(3)]

t3 = 150 N

hope this helps

Answer 2

see the attached figure with letters to better understand the problem

we know that

in the x-coordinates

$TACx=TBCx\\ TAC*cos60=TBC*cos30\\\\ TAC*\frac{1}{2} =TBC*\frac{\sqrt{3}}{2}$

$TAC=TBC*\sqrt{3}$ -----> equation $1$

in the y-coordinates

$TCD=150 N$

$TACy+TBCy=TCD\\ TAC*sin60+TBC*sin 30=150\\ \\ TAC*\frac{\sqrt{3}}{2} +TBC*\frac{1}{2} =150\\ \\ TAC*\sqrt{3} +TBC=300$

$TAC*\sqrt{3} +TBC=300$ -----> equation $2$

substitute equation $1$ in equation $2$

$[TBC*\sqrt{3} ]*\sqrt{3} +TBC=300\\ 3TBC+TBC=300\\\\ TBC= \frac{300}{4} \\ \\ TBC=75 N$

$TAC=TBC\sqrt{3}\\ TAC=75\sqrt{3} N$

therefore

the answer is

$TAC=75\sqrt{3} N\\ TBC=75N\\ TCD=150N$