Tricky trigonometric word problem

I've tried three different approaches to it, and it's taken me well over an hour and I CAN'T figure it out.

The pictures pretty much just for the diagram but in case you can't read the text.

19. The Great Pyramid of Khufu has a square base with a side length of about 230m. The four triangular faces of the pyramid are congruent and isosceles. The altitude of each triangular face makes an angle of 52 degrees. with the base. Find the measure of each base angle of the triangular faces to the nearest degree.

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