Question

All but two of the here amid’s built by the ancient Egyptians have faces inclined at 52° 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 m. How tall was the pyramid, assuming it’s faces were inclined at 52°? Round your answer to the nearest meter.

A) 25m
B) 32m
C)52m
D) 105m

Answer 1

Consider the cross-sectional right triangle shown in the figure.

One of its sides is the height of the pyramid, with length H. The other side is half of the square base, so its length is 81 m. The hypotenuse of this triangle is the height of one of the faces.

By right triangle trigonometry,


`\displaystyle{ \tan52^o= (H)/(41 \ m )`,

thus,


`H=\tan52^o\cdot41 \ m=1.28 \cdot41 \ m=52 \ m`.


Answer: C) 52 m