Forces-vector diagram triangles

[vadevalor]

when a cable car is stationary,it is in equilibrium.So the forces acting on it forms a closed triangle.(the vector diagram) Why is the triangle an isosceles triangle?

I did this question on my paper and stumbled across this on the answers,couldnt figure out why
hope someone could enlighten me!

 

[HallsofIvy]

I'm not the best person to be answering physics questions but I don't see that it is. Am I misunderstanding the question? I have the weight of the car, straight downward, a force due to the cable, perpendicular to the cable, and a component of force parallel to the cable, holding the car stationary. I do not see that this is an isosceles triangle.

 

[vadevalor]

hm..in your scenario it doesn't seem to be stationery to me,seems like the resultant force isn't 0 and is towards the opposite direction of the parallel force to the cable you mentioned. I'm referring to 3 forces that act on the cable car(weight and 2 tension forces at certain degrees to vertical and horizontal) to form a closed triangle since the cable car is in equilibrium. I can't get why the answer says when it is in equilibrium the triangle is isosceles.

 

[Saitama]

Make a Free-Body diagram, assume that the tension forces makes angles θ₁ and θ₂. Observe that the sin components equals (as the cable car is stationary) from where you can get θ₁=θ₂. You can then proceed further.

 

[Infinitum]

θ₁ is not necessarily equal to θ₂ in the way the OP has presented the question. You can have tension at different angles and still keep it in equilibrium.

For example, call the two tensions T₁=1N acting -30 degrees from the vertical and T₂=(1/√3)N acting at 60 degrees from the vertical with the cable car having a weight (2/√3)N.

If there is the extra condition that both the tensions are equal, then yes, you could say they form an isoceles triangle.