Part a: all but two of the pyramids built by the ancient egyptians have faces inclined at 52 degree angles. suppose an archaeologist discovers the ruins of a pyramid. most of the pyramid has eroded, but the length of a side of the square base is 82 meters. how tall was the pyramid, assuming its faces were inclined at 52 degrees? round your answer to the nearest meter.

25 m
32 m
52 m
105 m,

The height is 52m.

The height forms a right triangle with the slant height of the pyramid and half of the length of the square base.  Half of the length of the square base would be 41m.  The angle is 52°.  The sides we have are the height, which is opposite the angle, and half of the base, which is adjacent to the angle.  The ratio opposite/adjacent is used for the tangent.  Our equation would be:

tan 52=h/41

We multiply both sides by 41:
41*tan 52 = (h/41)*41
41*tan 52 = h

Evaluating this we get 52m.