Maths mech question

Hi, please could I have help on this question? I’m confused which angle the question is asking to work out, I thought it would be the angle right through the middle but I’m not sure and I don’t know how to work it out.
Here is the question: https://ibb.co/yfWnnRv
Thanks!

There are two tensions (equal) but at different angles down the slopes. So the resultant force due to those will make an angle with the vertical and is the force exerted on the pulley.

hi, thank you for your response, but I'm confused what and where the vertical is?

A vertical line through the pulley. The floor is horizontal, vertical is up.

i see, but I'm confused on how I would work out the angle because its not evenly split. Drawing a vertical line will produce two triangles so one angle would be 60 and one angle 30 but I'm not sure where the resultant force is located?

Thats what the question is asking. You should know how to add two forces together tip to tail and work out angle / magnitude for the resultant (diagonal), but as the tensions are equal, there is little maths needed, just a bit of reasoning about a standard triangle.

oh, but the markscheme says the answer is 15 degrees?

Which is correct. The resultant force (hypotenuse of the triangle when you add the tensions tip to tail) makes an angle of 15 degrees with the vertical.
Can you sketch the tip to tail tensions and hence the resulting triangle?

https://ibb.co/rxhZGyt This is my drawing

No. The angle between the two forces is 90, as you said earlier, so you when do tip to tail (vector addition) you first follow down the 60 right one (say) a length T, then at the end add the second T to it (so tip to tail) at 90 degrees. It obviously produces a right triangle with both legs of length T and hypotenuse is the resultant force.
Just google vector addition / tip to tail if necessary. It should be relatively easy, but it is important.

I’ve tried drawing it out again, the circled diagram and the one on the top right, not sure if they’re the same.
https://ibb.co/pQbdVgf
But I still don’t see where 15 comes from? Thank you.

For the string - pulley system, boht strings pull down on the pulley. The pulley pushes back upwards (roughly). For one thing yuo have the tensions drawn for the forces that act on the masses, not on the pulley. So its as in the picture. The original tensions acting on the pulley are the black lines, the red dashed lines represent the vector tip to tail (and resultant - hypotenuse) addition and described above.

Thank you for this, it makes more sense now! But where would the 15 be from ?

its an isosceles right triangle so 45-45-90. So the angle that the hypotenuse makes with the vertical is ...

The vertical line goes up vertically through the point where the two tensions originate from (the pulley).

so those that means in between the two black lines, but wouldn’t that be in line with the resultant force?

The right black iine (tension) is at 30 degrees to the vertical. The right triangle is 45-45-90 (right black line and 2 dashed red lines). The hypotenuse (red dashed) is the resultant force exerted on the pulley and makes an angle 45-30 = 15 with the vertical.

Sorry,I’m really confused where the 15 is from?