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Pythagorean Theorem And Its Applications

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Published in: Mathematics | Maths
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This is a 16 slide PowerPoint presentation to present the Pythagorean theorem, some practice examples, and real world applications on it.

Maged / Abu Dhabi

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Qualification: B.Sc. in Mathematics

Teaches: Mental Maths, Vedic Maths, Statistics, Maths, Arabic, English, Advanced Maths, Mathematics, GRE, SAT, ACT, EMSAT, IB Exam Preparation, Exam Preparation, Computer

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  1. The Pythagorean Theorem toolfor right triangle prob]err13
  2. When do I need to use the Pythagorean Theorem ? YYherj ] krjovy: length of 2 3jd93 Arjc] Need •to krjoyy: length of 3rd 3jde
  3. Whatis-the-Pythagoream Theoremy C Where a and b are legs and c is the hypotenuse
  4. Using a2+b2 • Looking forlength of the hypotenuse x 15 20 • 152 +202 • 225 + 400 = C2 625 = c2 625 =
  5. Using a2+b2 • Looking forlength of A leg x • 62 + b2 • 36 + b2 • -36 b2 64 = 102 -36
  6. Applying the Pythagorean Theorem
  7. A 15 foot ladder leans up against a building. The foot of the ladder is 5 feet from the base of the building. How high up the wall, to the nearest foot does the ladder reach? Draw a picture: 15 x 5
  8. Solving the problem 52 52 -25 -25 = 200 200 X = 14.142135 Write formula Substitute in Solve for x Check: How am I to leave my answer? The ladder reaches 14 feet up the wall.
  9. Tim rode 8 miles due north, then 3 miles due east. How far, to the nearest mile, is Timfrom wherehe started? • Draw a picture: 3 8 x
  10. Solve the problem 2 32 73 c 8.5440037 Remember: How am I suppose to leave my answer? Tim is 9 miles from where he started.
  11. FurtherAppIications The diagonals of a rhombus are 6 cm and 8 cm. What is the length of each side of the rhombus? Prior Knowledge: What properties does a rhombus have? The diagonals of a rhombus: bisect each other The diagonals of a rhombus: are perpendicular The sides of a rhombus: are congruent
  12. Draw a picture and solve: 4 4 x 3 rhombus is really 4 right triangles in disguise!- 32 + 42 • 9+16— • 25 = Each side of the rhombus is worth 5 cm.
  13. As seen inthe accompanying diagram, a person can travel from NYC to Buffalo by going north 170 miles to Albany and then west 280 miles to Buffalo. A) If a highway is built to connect NYC and Buffalo, how many miles would be saved on the trip ? B) With gas prices at $3.10 and a vehicle that gets 18 mpg, how much money would be saved roundtrip, if the new highway was traveled instead of the old route?
  14. Find length of new highway 280 mile. Albany 2802+1702-cr 107300 170 miles 107300 = c2 327.566= c Did I answer question'? New York City How many miles would be saved? Old Distance: 280 + 170 = 450 New Distance: 327.566 Saved Miles: 122.4 or 122 miles
  15. How much money can be saved? • Saved Miles: 122 miles x 244 • Cost to drive one mile (gas): • $3.10 divided by 18. ($0.1722...) • Cost to drive 244miles • $ 0.1722 times 244 • Saved: $42.02
  16. Wrapping It UP The Pythagorean Theorem be used only on triangles. When should the Pythagorean Theorem be used? What should be done first when solving a word problem involving the Pythagorean Theorem? What must be done before writing the answer to a Pythagorean Theorem problem? When the length of2 sides are known and the length of 3rd side is needed Draw and label triangle Check to see whether the answer should be rounded or not

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