AP calculus

posted by .

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!

3.
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

• AP calculus -

The answer is 1 in. = 2.5 ft
You're welcome.

Similar Questions

1. math

according to the smithsonian institute, many of the original stones were removed and or eroded. The length of one side of the square base originally measured 207 ft. less than twice the height. The original volume of the great pyramid …
2. measurements

The great pyramid of Giza was built around 2560 BC. It was originally 481ft high with a square base measuring 751 ft on each side. It's slant height was 611 ft. Find the lateral surface area of the great pyramid, round your answer …
3. geometry

The Great Pyramid of Giza was built around the year 2560 BC. It was originally 481 ft high with a square base measuring 751 ft on each side. Its slant height was 611ft. Find the lateral surface area of the Great Pyramid. Round your …
4. math

The pyramid of Giza in Egypt is built of stone and was completed in 2560 BC. The length of each side of the square base is 230 meters and the vertical height is 146 meters. 1. What volume of stone is needed to form a solid pyramid …

The Great Pyramid of Giza is 280 feet tall and about 440 feet wide at the base. The distance from the apex to the center of one side of the base is 356.1 ft. What is the area of one side of the pyramid?
6. math

A truncated square pyramid (also known as a frustum) is an object obtained by cutting a square pyramid by a plane parallel to its base (as shown in the figure). For a truncated square pyramid it is known that the side length of the …
7. Math

the great pyramid of cheops is a square based pyramid with a height of 147 meters and a base length of 230 meters. find the angle to the nearest degree that one of the edges of the pyramid makes with the base
8. math

Ira built a model of the Great Pyramid in Egypt for a school project. The Great Pyramid has a square base with sides of length 756 feet. The height of the Great Pyramid is 481 feet. Ira made his model pyramid using a scale of 1 inch:10 …
9. math

Ira built a model of the Great Pyramid in Egypt for a school project. The Great Pyramid has a square base with sides of length 756 feet. The height of the Great Pyramid is 481 feet. Ira made his model pyramid using a scale of 1 inch:10 …
10. Math

Ira built a model of the great pyramid in Egypt for a school project. The great pyramid had a square base with sides of length 756feet the height of the great pyramid is 481 feet Ira made his model pyramid using a scale of 1 inch :20 …

More Similar Questions