3-D Pythagorean Theorem - Pyramid.pdf

The Pythagorean Theorem in Three DimensionsWe know how to solve problems using thePythagorean Theorem in two dimensions.Let's review one now.1.

Now let's see how we would use the Pythagorean Theorem inthree dimensions2.

Now let's see how we would use the Pythagorean Theorem inthree dimensions2.slantheightslantheight**The slant height of the pyramid is always thehypotenuse of the right triangle.**The slant height should always be substitutedinto c in the formula a 2 +b 2 =c 2

3.Notice that in thisquestion they gave us theslant height and asked usto find the height**The slant height of the pyramid is always thehypotenuse of the right triangle.**The slant height should always be substitutedinto c in the formula a 2 +b 2 =c 2

4.3.5 fthalf of 7, the side of thesquare pyramida 2 +b 2 =c 23.5 2 +b 2 = 6.5 212.25 + b 2 = 42.25-12.25 -12.25b 2 = 30b = √30b is about 5.477b is about 5.5 ft

5.The base of a square pyramid is 10 inches and the height is12 inches. Find the slant height of the pyramid

5.The base of a square pyramid is 10 inches and the height is12 inches. Find the slant height of the pyramid

6. Some of the Mayan pyramids in Mexico are approximatelysquare pyramids. The one pictured below is 138 feet talland has a square base of about 160 feet. How long is thepath you would climb to reach the top to the nearest foot?

6. Some of the Mayan pyramids in Mexico are approximatelysquare pyramids. The one pictured below is 138 feet talland has a square base of about 160 feet. How long is thepath you would climb to reach the top to the nearest foot?cb80fta160ft138fta 2 + b 2 = c 280 2 + 138 2 = c 26400+ 19044 = c 225444=c 2√25444=c159.5 ≈ cyou would climbabout 160 ft

7.The error she made was using the slantheight in the wrong place in the formula.The slant height of the pyramid isalways the longest side of the righttriangle so it should be substituted inplace of "c". She used the slant height inplace of "b"

8.A pencil sits in a pencil holder that is a rectangular prism. The pencilsits on a diagonal inside the box. Using the diagram below, find thelength of the pencil to the nearest cm.Hint: This is a two step problem.8 cm3 cm4 cm

8.A pencil sits in a pencil holder that is a rectangular prism. The pencilsits on a diagonal inside the box. Using the diagram below, find thelength of the pencil to the nearest cm.Hint: This is a two step problem.8 cm3 cm4 cm