You just slid down a 900 ft zipline, to get back to the tower it’s 700 ft, how tall is the tower?

How to solve a right triangle word problem using the Pythagorean Theorem.
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[@Geoff_G]

Right angle triangle, so Pythagoras a² + b² = c² Zip line is side c, the ground is side a, solve for side b. b² = c² - a² b² = 900² - 700² b² = 810,000 - 490,000 b² = 320,000 b = √320,000 b = 565.685 -edited for typo in the word "solve"

[@TheTechnofu]

why is it that you can say that in a few minutes and ALL math teachers have to interject unrelated stories after every segment. I'm all focused and it's wasted on stories! Do they train math teachers to do that? it doesn't make it less boring - just takes longer and more frustrating!

[@carolleenkelmann3829]

You mean to tell me, 200 ft is wrong?!😱- I shall never forget our geometry teacher, Mrs Breed. The first thing we ever started out with was this example. Now wasn't there a rule to cancel out the shared 00's and the squared signs? That would make it so much less complicated.

[@UrsaNiagara]

... should say it's a 700' WALK back in the test.

[@simonsimon9880]

Why? It's also 700' if you drive. 700 feet is 700 feet, no matter how you get there. 🤷‍♂️

[@m.h.6470]

Solution: This is a right angle triangle, so use Pythagoras: 700² + h² = 900² |-700² h² = 900² - 700² |3. Binomial h² = (900 - 700)(900 + 700) h² = 200 * 1600 h² = 2 * 16 * 100 * 100 h² = 2 * 4² * 100² |√ h = √2 * √4² * √100² h = √2 * 4 * 100 h = 400√2 ≅ 565.69

[@gillianrolland4305]

Much better way if doing the calculation than him

[@paulpurpura191]

Hey John! Your favorite 72 year old math student here. The exact answer to the problem is 400 times the square root of 2. I really enjoy your videos and doing the math problems. They clear out the cobwebs in my brain.

[@philipmumford7871]

much better answer - he should have factored it immediately to get rid of the root 2 and all the zeros!

[@vespa2860]

Lazily looked and sort of figured the return to the tower was returning to the point of departure - an Escher-like vision opened up!

[@Ganja-jh6iy]

It's more complicated than that. You need to take the cantenary function into account . That is unless the cable has no sag.

[@taknothing4896]

He explicitly said it was a straight line, therefore no sag. But yes, not realistic.

[@elfishcoder7287]

No it isn't. This type of question would be something you'd encounter in secondary school.

[@RandyMcFarland]

Well, if that what you'd expect with a simple math question, I guess you should research the average slack there is in most ziplines and continue your calculations...

[@Ganja-jh6iy]

@@RandyMcFarland expect nothing and assume nothing that's what momma always taught me.

[@granitegrizz]

Whereas I was focusing on the fact that you don't get off a zipline against at ground level. You usually get off when the line around your height.

[@7373robin]

Does not tell the height of the tower just the point where the zip line is attached to the tower.

[@robertstuart6645]

The answer is 566 feet, rounded.

[@tomtke7351]

My history of zip lines is they start from a geographically higher point to land at lower. Apparently this problem ASSUMES the zip line starts from the top of a tower that starts at same elevation at lsnding.

[@Davidbmr1970]

565.69 feet.

[@MrMousley]

We have a right angle triangle here ... Pythagoras ! The zipline is the hypotenuse and the distance from the tower is one of the other sides. So the answer is Height squared + 700 squared = 900 squared Height squared = 900 squared - 700 squared Height squared = 810,000 - 490,000 Height squared = 320,000 Height = square root of 320,000 Which (calculator time !) is 565.685 to three decimal places.

[@vincentrobinette1507]

To do this in my head, I deleted the 2 "0"s, and made it 9 and 7. 81-49=32 the squared root of 32 is 5.6568. Just move the decimal over 2 spaces to arrive at 565.68. (I did use a calculator to get the square root of 32)

[@edwardnagel7598]

That's almost a 45 degree angle. You're approaching terminal velocity at that point.

[@patrickmarshall4142]

I can't find the exact quote, but an engineering professor made minor poetic history when he accidentally rhymed speaking of catenaries with something like: "No matter the weight, or the tension so great, can you get a line that is absolutely straight". So no, not a realistic analysis, even for a line that has no load. It can be calculated if you add the weight per unit of length and the tension, but not with the Pythagorean theorem.

[@alwayslearningthankyou2708]

565 ft 8.225"

[@1721craig]

so if one could calculate and vocalize post mortem then the answer is approx. 565.68 feet, at least to answer the screenshot question. the professor here explains how we get to that answer by oversimplifying

[@devonwilson5776]

Greetings. I honestly didn't have the foggiest idea as to what a zip line is. However, I was thinking along those lines as represented by your sketch. Now, the entire this is crystal clear. Finding the height of the tower is like taking candy from a baby. Using a^2+b^2=c^2, a^2=c^2-b^2. That is a^2=900^2-700^2=810,000-490,000 =320,000=400×800, and a =20 times the square root of 800 ft., or 565.7 ft.

[@PlasmaCoolantLeak]

I enjoyed problems like this in my college pre-algebra and algebra classes. Too bad I didn't when I was in junior high and high school.

[@johnnyllooddte3415]

somewhere between 500 and 600 ft

[@emjkenny]

I'm dyslexia. I can't understand this question. Tower it's 700ft... What is 700ft? Where are the commas? I've no idea what this question means. I'm guessing you go down the zipline into the rapunzel window at the top, so the answer is any height. No info in the question to possibly answer this.

[@frowe327]

Someone commented that the catenary sag needed to be taken into account. We must assume that there is no sag for simplicity's sake. If SAG needs to be taken into account, then are the weight of the writer should be given!

[@vespa2860]

5:35

[@stevem5383]

How much sag is in the zip line?

[@danieldennis9831]

√2•400 or about 565.5 ft

[@Surreal_Wizard]

Hmm... I get roughly five hundred sixty five feet and eight point twotwofive inches tall. I musta done something wrong. Well, I suppose 565.6854 feet is correct if you are using surveyor's units, but I was going with architectural units of feet and inches, which corresponds to 565'- 8.22".

[@johnbollenbacher6715]

I think the title of the video should say that the zip line is taut. otherwise, the problem is much different to solve.😊.

[@johnpauly5524]

…it’s 700’ He tells you that in the equation Tower is 700’tall🧐

[@simonsimon9880]

Trick question. If you just slid down a 700' zip line at 38°, you are now dead.

[@mangomachineshop7525]

1140.18

[@user-gv1bf2hy6p]

Can only solve if you assume the ground and the tower are at 90 degrees. Does it say they are?

[@garyalabama]

Exactly. I felt it was insufficient information. I don’t see where it says the tower and ground are 90 degrees

[@simonsimon9880]

The diagram is pretty clear. Nor sure what your confusion is.

[@garyalabama]

@@simonsimon9880what diagram, I only see a problem statement. He added a drawing but that wasn’t in the problem statement. You could easily have the pole in a hill and land well below the pole

[@user-gv1bf2hy6p]

@@garyalabama Correct. The diagram is not part of the question. It is part of the solution.

[@remessinger]

No zip line for me. 😁

[@frowe327]

565.6 ft

[@mahamunibalakrishnan8263]

565.4 '

[@motorbuzz4748]

I got 178.8 feet

[@russelllomando8460]

Got it. P therom. You could have made it easier with triplets 4:16 4:52

[@stevedietrich8936]

178.8 Edit: Oh crap I did the math in my head and missed a zero and had the square root of 32000 instead of 320000. Shades of sloppy errors just like in high school.

[@annetomasso1155]

This is the worst writing in a math problem I have ever seen. You have a comma splice joining what should be two separate sentences. And then you have a missing period which creates a nonsense sentence. Many will not be able to understand the problem based on that. You may get an A in math, but you earned an F in grammar and logic.