Isaac Physics Question

https://isaacphysics.org/questions/floating_on_mercury?board=y12ms2019_20_week06See it here. I'm stuck, as I'm not entirely sure what angle I am supposed to find in order to find the relationship between the similar triangles

bump

By bumping your own thread would not help in most of the circumstances especially it is within the same day.
The best way is always to describe your confusion in detail and tell us what have you gotten in attempting the problem.


You can work out to find the angle θ₃, as shown in the picture. The diagram is NOT DRAWN TO SCALE.

Thanks for the reply. I have gotten the angle to be 30.34 degrees. Then I have resolved a triangle taking the height as 2.5cm to give the length of 1.463cm. Adding this onto 2.5cm from the 45 degree triangle in the bottom right corner has given d equal to 3.963. I'm not sure if my process is correct though. Thanks

I cannot really understand your "working". It would be better that you make labels to your calculations.
For θ₃ to be 30.54 deg, d cannot be 3.963 cm (if I did not misunderstand what you described) as this does not make sense.

https://imgur.com/9xLDoK3 See this

If θ3 equals 30.54, and h equals 2.5cm, then we can separate one triangle into two triangles and add the bases. 2.5Tan(30.34) + 2.5tan(45) gives us 3.963cm...

Your θ₃ in here is different from what I implied in my drawing in post #3.

In my drawing in post #3, θ₃ is the angle between light ray (black line) and normal (light blue line) and you change the meaning of θ₃ in your own drawing in post #6.

Right. How can I get the base from theta 3 considering that it doesn't form a right angled triangle?

Not really sure I understand your question.
You can see there is a right-angled triangle as shown by the dotted yellow lines in the diagram below which involves θ₃.


I highly recommend that you re-draw your own diagram to understand the various angles and the given info.

https://imgur.com/R6rXWGi

Considering that right angled triangle you drew, and the sketch I have made of it, I am trying to find angle X to get the base of the triangle. Angle X consists of theta 3 + another angle (let this be alpha), (the one between theta 3 and h in your diagram). How do I find alpha, considering I have no other information.

Theta 3 on its own does not make a right angled triangle, it makes a triangle that looks like this https://imgur.com/z1GWwfC. The red is the right angled triangle you drew

You really need to relook on the diagram that I had drawn.
The yellow dotted line triangle DOES NOT correspond to the partial red triangle you had drawn.
This is why I mention you should redraw the diagram on your own (using paper, pencil and ruler) to better understand the angles instead of just “blindly” applying my diagram. My diagram makes sense to me but it may not make sense to you if you don’t really understand what I am drawing.

Don’t be too quick to reply. All the info is really in the diagram if you really draw on your own and fill in your own labels which I did not label. Do not rely on other people diagram to solve the problem. Draw your own to make sense or else you are blindly searching for an answer.


Below is the diagram that I have shown in post #9.