prove the height of the pyramid of khafre find the height of a square based pyramid knowing the base...
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![Page 1: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/1.jpg)
Prove the Height of the Pyramid of Khafre
• Find the height of a square based pyramid knowing the base dimensions and angle of incline.
aa
![Page 2: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/2.jpg)
• Start by splitting the base in half with a right angled line.
a/2 a/2
![Page 3: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/3.jpg)
• Second, split one of the side up the middle.
a/2 a/2
ө
![Page 4: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/4.jpg)
• Thirdly, draw a line from the tip of the pyramid to the center of the base. This is the height.
h
a/2 a/2
ө
![Page 5: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/5.jpg)
• There now exists a right angled triangle with a known base and angle of incline.
ө
h
a/2
![Page 6: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/6.jpg)
• Therefore, the height of the Pyramid of Khafre is 143.8m
ө
h
a/2
Calculate h when:a = 215.5mө = 53.16°
tan ө = opposite / adjacent
tan 53.16° = h / (215.5/2)
h = tan(53.16°) x 215.5 / 2 = 143.8
Prove the Height of the Pyramid of Khafre
![Page 7: Prove the Height of the Pyramid of Khafre Find the height of a square based pyramid knowing the base dimensions and angle of incline. a a](https://reader036.vdocuments.net/reader036/viewer/2022071807/56649e875503460f94b8a36b/html5/thumbnails/7.jpg)
Calculate the height of the Pyramid of Khufu
• Measure the base dimensions of Pyramid of Khufu using in Google Earth.
• The angle of incline is 53°50’40” (53.84°)
• Verify your answer by using the measure tool in Google Earth.