I Calculating change in length for a projection

[Furious_George]

I haven't touched a physics textbook in a while and need help with something fairly simple. I am staring straight down on a rectangular prism that is tilted on one axis to a known angle, theta. I have a measurement of a vector length in this orientation. I would like to know how much that length changes with respect to theta. What is the increase in length when theta becomes zero?

 

[Nidum]

Draw the end view and you should see the solution immediately .

 

[Furious_George]

Draw the end view and you should see the solution immediately .

The image on the right is the end view. My issue is that I need to back this up mathematically - I need more justification beyond just a picture and I need to calculate an uncertainty later on based off of my numbers.

 

[Ibix]

I think @Nidum means a view of one of the left or right hand ends (as we're looking at it).

 

[Furious_George]

I'm also not sure what terminology I would google to find a solution. Am I projecting an vector onto a plane here? Or does that imply that I am not changing my length (which I am in this situation). What equations can I use to solve this?

 

[Ibix]

Draw the diagram Nidum suggested. Mark on it the length you know and the distance you want to know. Hopefully the answer will be immediately obvious from high school maths (hint - there ought to be a right angle somewhere). If not, take a photo if your diagram (in good light!) and upload it and we can see where you've got to.

 

[Nidum]