IM 8.8.10 Lesson: Applications of the Pythagorean Theorem
Which estimate is closest to the actual value of the expression?
[math]\sqrt{24}[/math]
Explain your reasoning.
[math]\sqrt{7}[/math]
Explain your reasoning.
[math]\sqrt{42}[/math]
Explain your reasoning.
[math]\sqrt{10}+\sqrt{97}[/math]
Explain your reasoning.
[size=150]Mai and Tyler were standing at one corner of a large rectangular field and decided to race to the opposite corner. Since Mai had a bike and Tyler did not, they thought it would be a fairer race if Mai rode along the sidewalk that surrounds the field while Tyler ran the shorter distance directly across the field. The field is 100 meters long and 80 meters wide. Tyler can run at around 5 meters per second, and Mai can ride her bike at around 7.5 meters per second.[/size][br][br][img]data:image/png;base64,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[/img][br][br]Before making any calculations, who do you think will win? By how much? Explain your thinking.
Who wins? Show your reasoning.
A calculator may be necessary to answer the following questions. Round answers to the nearest hundredth
If you could give the loser of the race a head start, how much time would they need in order for both people to arrive at the same time?
If you could make the winner go slower, how slow would they need to go in order for both people to arrive at the same time?
Here are two rectangular prisms:
[img]data:image/png;base64,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[/img][br][br]Which figure do you think has the longer diagonal? Note that the figures are not drawn to scale.
Calculate the lengths of both diagonals. Which one is actually longer?
IM 8.8.10 Practice: Applications of the Pythagorean Theorem
A man is trying to zombie-proof his house. He wants to cut a length of wood that will brace a door against a wall. The wall is 4 feet away from the door, and he wants the brace to rest 2 feet up the door.
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[/img][br][br]About how long should he cut the brace?[br]
[size=100][size=150]At a restaurant, a trash can’s opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada’s explanation? Explain your reasoning.[/size][/size]
Select all the sets that are the three side lengths of right triangles.
Which of the two numbers is larger?
[math]12\cdot10^9[/math] and [math]4\cdot10^9[/math]
[size=100]How many times larger?[/size]
[math]1.5\cdot10^{12}[/math] and [math]3\cdot10^{12}[/math]
[size=100]How many times larger?[/size]
[math]20\cdot10^4[/math] and [math]6\cdot10^5[/math]
How many times larger?
[size=150]A line contains the point [math](3,5)[/math]. If the line has negative slope, which of these points could also be on the line?[/size]
[size=150]Noah and Han are preparing for a jump rope contest. Noah can jump 40 times in 0.5 minutes. Han can jump [math]y[/math] times in [math]x[/math] minutes, where [math]y=78x[/math]. [/size][br]If they both jump for 2 minutes, who jumps more times?
How many more?