A ladder’s max angle is 75 degrees for safety; how long of a ladder is needed to reach 90 ft?

How to solve a right triangle trigonometry word problem.
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[@GrantOakes]

5:45 mark, 95 degrees would have the ladder falling over away from the building, assuming that 90 degrees is straight up and 95 degrees is an obtuse angle. YES, I AM paying attention!

[@JohnnyHughes1]

Correct.. and not possible in a right triangle. The two OTHER angles in a right triangle add to 90, so both must be 90 or less.

[@GrantOakes]

Changed my mind, I'm taking the elevator! 9 stories up, on a ladder? You're NUTS!

[@MoonKid79]

i just wanted to say how much i appreciate your channel! i just started a harder math program and your videos really helped. thank you!

[@devonwilson5776]

Greetings. The length of the ladder that is required to reach 90' up the wall when the foot of the lader makes a 75 degree angle with the ground is 93.2 feet. The solution is obtained by using trigonometric principle of Sin theta, theta being the angle between the base and the hypotenuse, equals the opposite side of a right angled triangle over its hypotenuse. From the details given, we need to find the length of the hypotenuse, the length of the ladder. We will assume that the length of the ladder is represented by X. Now, we have Sin 75 degrees equals 90/X, and XSin75=90. Moving on, X=90/Sin 75, X=90/.96592582=93.1748562=93.2 feet, rounded. Lovely.

[@tcz7742]

1973, first year university, I bought an HP-35 . The gold standard of the day . $500.

[@glennwright9747]

@@tcz7742I’m still using my HP32S

[@hotwireman49]

Oh joy! Rapture! I love you!!❤❤❤❤ I subbed. Thank you!!

[@terryjohinke8065]

Got it! ( ex Maths teacher and twin bro. was a surveyor)- answer is 93'2"

[@renebouman7513]

Those lovely old days, last week I discovered my old high school book of tables, never used it again after I got my first calculator in '73

[@glenwardgross366]

John can you do a video on how to figure out Sin 75 degree without the charts in the back of the math books and calculator? Also, how do you calculate pie by paper?

[@russelllomando8460]

We had to walk uphill, both ways... Got it all, diagram, formula, and soh, cah, toa, just didn't have the calc for the sin. I'm happy I got as far with my knowledge. Great problem.

[@user-zu6qn9ux9n]

Answer: A bloody big one!

[@tonidozier4573]

My drawing and problem setup was correct (I was thrilled), especially since I haven’t been exposed to this info in several years. I used radians (why?) when I got Sin 75°.

[@Geoff_G]

Well, there's about 2' overlap in each fly section of the ladder. The longest fly section is generally about 20". And of course, there are the extra 4 rungs about the step off point. So, a 120' six fly section extension ladder. And that ladder would need some amazing tormentor poles.

[@GrantOakes]

I did it by taking the tangent of the opposite angle, 15 degrees X 90 squared, adding to square of 90 nad then the square root of that and you get a tad over 93'.

[@fionam3554]

That 30* angle is dangerous. Center of gravity is far from the foot of the ladder and the force of gravity on it is DOWN. The feet are going to slip unless you anchor the heck out of them (like a fire truck ladder, the truck won't slide) and the leverage is going to stress the heck out of the ladder material- aluminum likely holds, wood likely doesn't and snaps if the person is heavy)

[@renolds531]

A 90 foot ladder is needed to reach 90 feet, irrespective of the angle.

[@mda7763]

Wrong

[@glenwardgross366]

Safety 1st, 2nd, 3rd. If you do not understand the 3 rules then read them again. If you do not understand the rules then you need to leave now. Please if you need a ladder to work then follow the 75 rule because it will save your life. I think John has lost it..... A 90 ft building is basically a 9 story building. What home improvement store carries ladders this size? We are looking at a 100' ladder placed at a 75 degrees opposite the 90 degree right angle base with 15 degree @ the top angle. Home improvement stores sell ladder that are two sectioned. John's ladder would have to have 10 sections to reach the top of the 90' building. Two piece ladders are rated @ 300 lbs. each section is 10 ft. @ 10 sections what would the safe lbs for someone brave enough to climb the ladder to put up the Xmas lights on the building. Just for fun. Blessing

[@mda7763]

Important note You cannot enter Sin(75) into your calculation The correct way is 75Sin. Enter 75 then hit the sin key

[@stevenscottoddballz]

Steve Demme teaches: "What do you do if you stub your toe badly? You SOH-CAH-TOA. [soak a toe]"

[@lakeireland]

After living in the South for 23 years, I know the answer a 70’ ladder with a 20ft ladder tied to it. (Seriously, don’t do that, you’ll break your head )

[@GrantOakes]

hahahahahaha! You even added that you're from the South, had me in stitches!

[@ganggreen9012]

You need a 90' ladder on top of a 3' table.

[@pixelpatter01]

If you have ever climbed a 90 foot ladder you are in a small group of human beings.

[@mikemassey7403]

You got that right. I have enough sense to NOT climb the damn thing.

[@juergenilse3259]

I wouldn't do that.If needed, i would pay someone for it ...

[@roy40ss]

A much easier way to remember is “see old Harry, catch a herring, trawling off America” 😀

[@JackSprat-vk1nz]

Is the adjacent side approximately 24.11ft?

[@JackSprat-vk1nz]

I tried to follow along but my calculator kept giving me .12 or 1.2 The problem was you said 90 divided by sin 75 but on my phone the 75 has to be put in before the sin button.

[@muchomacho2504]

Back in MY day, calculators were called "slide rules"

[@JohnnyHughes1]

Scientific Calculators ..heh. Now do it with a Sin table and slide rule.😊

[@simmo5071]

93’

[@TheRitchieLeeShow]

A very long ladder😂

[@juergenilse3259]

better longer than to short??? The you may prefer a 250 feet ladder?

[@pesky4649]

A little over 93 ft.

[@stevemccready6776]

The correct answer is anything over 40' is not Osha approved

[@davidloewen5528]

I doubt anyone makes ladders in increments of less than one foot. Probably should have gone with metres, might have avoided that OSHA comment. That one rules.

[@user-ri6rn7ti5h]

93.17

[@juergenilse3259]

... is a little bit to short(as the exact answer is 93.1748...). Better do not round correctly but always round up in this case ...

[@generalmanagerformays587]

I actually got 93.1773 but rounded it up to 93.18

[@juergenilse3259]

The exact value is 90*(sqrt(6)-sqrt(2)).You can get this result, if you know, that sin(75°)=(sqrt(2)+sqrt(6))/4 ...

[@Jabba1973]

This result seems to indicate you are using an angle slightly below 75° (74.9943928798895° to be more specific)

[@ozfire7]

93.16 ft

[@camdeskjockey2355]

Though I got the right answer, the better answer is get a boom truck. LOL

[@mikechappell4156]

Was SOH-CAH-TOA supposed to be easy to remember or something. Really didn't need a trick to remember sine=opposite/hypotenuse, cosine=adjacent/hypotenuse, tangent=opposite/adjacent, if I did, SOH-CAH-TOA wouldn't be it.

[@janettweed2701]

15 ft

[@dakotaiv]

I'm using the Sine (SIN) function in Excel. In Excel, SIN(75) = -0.387781. What am I doing wrong?

[@robomonkey6219]

You're using radians instead of degrees.

[@devonwilson5776]

Greetings. Funny that you would say that. I was using one calculator and turned up with the same value. When I divided 90 by that figure the answer obtained was ridiculously high and so I was led to think that something was wrong. In addition, the minus was a tip off. Thereafter, I checked another calculator and received a different figure that was more palatable and decided to go with the more reasonable solution.

[@MathsMadeSimple101]

Why on earth would anyone climb a ladder that long.

[@ndailorw5079]

@MathMadeSimple 101 …to see how it looks and feels to climb up a ladder that’s leaning at a 75° angle up against a wall, or something…? …couldn’t resist.. lol!

[@notreallydavid]

'How long a ladder...?' - no 'of'. Please kick me All best.

[@stevedietrich8936]

108 Edit: :( I hated trig and basically tuned out, as my answer shows.

[@alastairgreen2077]

How long a ladder, not long of a...

[@harrymatabal8448]

Ok a ladder is in the shape of a rectangle with each rung parallel to each other and at 90^0 to the 2 uprights. I can't see a ,75^0. Please clear my confusion. By the way I hope you didn't fall from a ladder and bump your head on a stone. Ok

[@user-ri6rn7ti5h]

13728

[@juergenilse3259]

at least not to short, but a ladder of this length would be very difficult to handle ... 😏

[@Kerbeygrip]

I live in Europe what are ft?

[@djholro]

1 ft = 30 cm 90 ft = 27 m

[@juergenilse3259]

@@djholro No. the exact factor to convert feet to eters is 3.048, so 90 ft is about 29 m and 53 cm.1 ft is about 32.8 cm, not only 30 cm ...

[@djholro]

@@juergenilse3259 i was just giving a ballpark figure. Accuracy means nothing to someone who can't envision what a foot is. If you want to be more accurate, sure. Use 30.48 cm. That still makes 90 ft = 27.432 m.

[@juergenilse3259]

@@djholro 3.048 feet are 1 m,1 feet is 1/3.048 m, which is about 0,328 m or 32.8 cm. So 90 feet is about 29,53 m, not only 27.432 m ...

[@djholro]

@@juergenilse3259 you're using the wrong conversion factor. 1 m = 3.281 ft. That does NOT mean 1 ft = 32.81 cm. Google it.

[@user-ec9ut2qr2s]

90 feet.😊

[@juergenilse3259]

A 90 feet ladder reaches only a height of nearly 87 feet (at an angle of 75°), so you have to bypass the last 3 feet without the ladder ...

[@user-ec9ut2qr2s]

@@juergenilse3259 No. A 90 ft ladder stood vertically reaches a height of 90 ft. Cannot climb it without bolting it onto the wall, but chimney ladders are fixed that way, just ask Fred Dinah the Steeplejack.

[@juergenilse3259]

@@user-ec9ut2qr2s It was asked for a ladder standing in an angle of maximal 75° to the ground. that was given as part of the excercise.With a 90 ft ladder standing in an angle of 75°, you reach a height of a little bit less than 87 ft.

[@richfrazier8756]

Not 90 degrees, 90 feet!

[@keithschipiour4684]

I will figure that out when the govt leaves me a million dollars on 90ft roof and I have to retrieve it.

[@timothybloomer4246]

"How long of a ladder?". Clearly not an English class.

[@Nikioko]

What is 90ft?

[@MathsMadeSimple101]

First.

[@keithschipiour4684]

I dont care. If ladder does not seem stable at whatever angle ladders position is I am not climbing ladder . It's called common sense math

[@henkhu100]

Why do you make things so difficult? What has the fact that a^2+b^2=c^2 to do with the solution? All these extra things are rather confusing for a lot of students. Just using sin = O/H so sin(75degr) =90/x is enough to find the solution. The rest has nothing to do with finding the answer. Don't make math more difficult than it already is for many people.

[@steventaylor7716]

It's time to put all trust in Jesus Christ.

[@generalmanagerformays587]

93.18 ft