How Do You Calculate the Angle \(\gamma_{xy}'\) in a Modified Rectangle?

[Saladsamurai]

[SOLVED] Finding an Angle (more trig)

(#25) Okay, so I am getting a little better at this, but still not great. I have to find the angle $\gamma_{xy}'$

I have drawn the original rectangle in blue and the new elongated one in green (I exaggerated it to help clarify)

Looking at points C and C' I can see that $\gamma_{xy}'=180-\tan^{-1}\frac{300}{2}+\theta$ where theta is that little bit more. . . that is between (BC)' and the vertical. If I could find that I would be all set.

Any ideas on how to proceed? Or should I have taken a different route?

My professor's hint says 'Find the sum of the angle change of both sides AB and AD'

which I thought is more or less what I am doing?

Thanks,
Casey

 

[Saladsamurai]

Super awesome. Maybe it's obvious to everyone else. . .

 

[mezarashi]

Hi, I'm not sure which angle exactly you want to find.

You can automatically find angles DAD' and BAB' from using tan.
Then you can use the 90 degree rules to find angles in between.
Along the way you can use the internal angles summation is 360 for 4-sided shapes and 180 for triangles.

If you assume that angle C'D'C is equal to angle B'AB, and assume angle DAD' is equal to angle CB'C', you'll have more to work with.