I've been working through a trigonometry book and have been stuck on the following question for a while now.
The diagram shows a roof structure. PQRS is a horizontal rectangle. The faces ABRQ, ABSP, APQ and BRS all make an angle of $45$ degrees with the horizontal. Find the angle made by the sloping edges with the horizontal*
The answer they're looking for is $35.26$ degrees.
I believe that this angle is $AQC$ where $C$ is the point directly below $A$. In order to find this the hypotenuse length $AQ$ is needed and either the height $CA$ or width $QC$.
I've started by finding the sloping lengths of the middle of each face, because there's a $45$ degree angle the height/width will be the same so I tried substituting in $1$ resulting in a sloping length of $2$.
Using the width / face slope I tried calculating $AQ$ by creating a new triangle halving the $PAQ$ face with a height of $2$ and width of $1$ which gives $AQ$ as $2.2$. The length $QC$ comes out as $2$ using Pythagoras.
These values for the triangle $ACQ$ give me an angle of $24.6$ degrees which is incorrect.
I think either my idea of substitution is wrong or the way I'm breaking up the structure.
Any ideas / hints would be greatly appreciated, thank you.