Posted by Layka on .
The base of the Great Pyramid at Giza is a square that is 230 m on each side.
1.Find the height of the pyramid, knowing that when a person is standing at the center of its side he measures the angle of elevation of the apex to be 51 degrees with an error of +/- 0.5 degrees.
2. Build the model of the Great Pyramid at Giza using calculations from #1.
3. Use differentials to estimate the allowable error in the elevation angle that will ensure an error in the height is at most +/- 5m.
AP calculus -
1. h = 115 tan51° = 142 m
with error, 139.51 <= h <= 144.57
2. sorry, you'll have to do that yourself!
h = 115 tanθ
dh = 115 sec^2 θ dθ
5 = 115 * 2.525 dθ
dθ = .01722 = 0.986°
just as a check, our error of ±0.5° indicates a height error of
dh = 115*2.525*0.5*π/180 = ±2.53m which agrees quite nicely with the explicit values found above