Pythagoras Theorem
Testo Storyboard
- Diapositiva: 1
- Elizabeth is going to her friends house to celebrate his birthday. She will need to arrive before 2.6 (2hrs, 36 min) hours or she will miss the party. She can either walk the long path to his house at 10 meters per hour or drive the direct path to his house with traffic at 8 meters per hour. Which path will get Elizabeth there in the least amount of time?
- Diapositiva: 2
- This is a map from Elizabeth's phone showing the distances between her location and her friends house by the direct street or the walking path.
- Friends House(12, 20)
- Direct street
- Walkingpath
- 16 meters
- 12 meters
- Elizabeth's location(5,9)
- Corner of walking path(12,9)
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- Diapositiva: 3
- This map shows the shape the paths make is a right triangle. Therefore, we can find how long the district street is using the Pythagorean Theorem.
- Friends House(12, 20)
- Direct streetc
- Walkingpath
- 16 metersb
- 12 meters
- Elizabeth's location(5,9)
- a
- Corner of walking path(12,9)
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- Diapositiva: 4
- The Pythagorean Theorem states a^2+b^2=c^2 for any right triangle. Now we will use this to solve for the length of "c" on the map where c is equal to the length of the district street.
- Plug in the numbers 12^2+16^2=c^2simplify 144+256=c^2Now, square root both sides √400=√c^2√400=c 20=cThis means the direct street is 20 meters long.Now we need to find how many hours it will take Elizabeth to travel. We know she travels at 8m/h on the driving path and 10m/h on the walking path. To find the time it takes Elizabeth we will use t=meters meters per hour
- t=time in hours
- Walking Patht= (16+12)/10t=28/10t=2.8 hours
- Driving Patht= 20/8t=2.5 hours
- The driving path will take Elizabeth less amount of time at 2.5 (2 hours, 30 min) hours.
- Diapositiva: 5
- Elizabeth is nearly out of gas. She will need to find the nearest gas station. According to her phone, the nearest gas station is halfway between her location and her friends house. Elizabeth is on the direct driving path. She is at (5,9) and her friends house is at (12,10). She only has enough gas to drive (4,1) more coordinates. Will Elizabeth be able to make it to the gas station?
- Diapositiva: 6
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- We know the location of the gas station is halfway between (5,9) and (12,10). TO find halfway or the midpoint we can use the midpoint formula. M=(x1+x2//2 , y1+y2/ 2)
- (5,9)= (x1,y1) (12,10)=(x2,y2)Plug in the numbers M= (5+12 , 9+10) 2 2Simplify M=(17/2, 19/2) M= (8.5, 9.5)
- The gas station is at (8.5, 9.5). Now we need to find the difference in her location and the gas station. (8.5-5, 9.5-9)= Coordinates away from gas station.Elizabeth is (3.5, 0.5) coordinates away from the gas station. She only has enough gas to travel (4,1) more coordinates. Therefore, she will have enough gas to arrive at the station.
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