there is a easy way, mirror the triangle around the pole. Top angle is 30 +30 so all angles are 60 degrees so the sides have to be the same. The pole is the middle to 100/2 no trig but geometry instead.

@quadmachine8434

4 ай бұрын

Did you wait for the whole explanation

@harrymatabal8448

4 ай бұрын

Graham if you say your method is easier than mine, I have no problem because you explanation and your answer is correct and to the point. Well done. Did it take you 20 minutes

@larrydickenson8922

4 ай бұрын

That is why the sine of 30 degrees (or the cosine of 60 degrees) is 1/2.

@grahamwise5719

4 ай бұрын

about 10 seconds, I'm in my mid 60s and geometry is source for lots of maths. I had to do exams without a calculator and had to use log tables and later a slide rule.

@grahamwise5719

4 ай бұрын

I worked my method first, then watched the video until I saw the method and thought mine was easier. I don't watch after I know the method.

SOHCAHTOA…..Brings back old memories from high school. Thanks!

Took me 30 seconds to find 'x'. Mirrored the triangle. All angles 60°. So all sides are equal. Pole in the middle of base which is 100 ft. So half of base = 50 ft. I'm 81 years old. Brought back memories from 1956. 😊

@MrSummitville

Ай бұрын

That was a good "trick" ...

thanks for the refresher

It's half an equilateral triangle, so x = 100÷2 = 50. Or if you prefer trig, cos60 = 0.5, 0'5×100 = 50 Either way works, but the trig generalises.

You catch me out every time I think I’ve got it. Thank you

It’s very simple. Consider figure is one isosceles triangle, where one length is 100 ft. So each arms are equal and 100 ft. Distance x = 100/2 = 50 ft.

Damn you take forever to get to the problem.

@brazillady5119

4 ай бұрын

Amen! Just get to how to solve the problem. All the extra stuff just confuses me.

@lwh7301

23 күн бұрын

He's extremely long winded.

The given picture is 1/2 of an equilateral triangle. Redraw the given triangle as an equilateral triangle. All sides are now equal in length, which is 100 each. Now, draw a circle which touches the three corners of our equilateral triangle. Note that the center of this circle has to be at the given 90 degree point for this to happen. Since the radius of this constructed circle is 50, you have unwittingly defined the radius to the top of the flagpole, which also touches the circle. Thus, the flagpole answer is 50.

@terry_willis

4 ай бұрын

I think you over worked it. Once you draw the equilateral triangle, you can see that the new base is one of 3 sides of the equilateral triangle, and is also 100". So X is one half of the base or 50'. I don't see that the circle adds any info to this. Plus, how do you know the radius is 50'?

@Astrobrant2

4 ай бұрын

The radius is not 50.

@terry_willis

4 ай бұрын

@@Astrobrant2 You may be correct. I stopped reading when he got to the circle part. After that he said, "Since the radius of this constructed circle is 50, you have unwittingly defined . . ." that's where I got the 50. Sorry.

crystal clear

50 ft. was my guess, but I didn't really understand how to calculate it. Thanks.

how i guessed it was that if it is a equilateral triangle then all sides are equal. si half of the 100ft is 50 feet.

How long is the pole?

Since this a 30-60-90 triangle, the height of the pole is 100*sqrt(3) and the base x is 100/2=50! So b is the answer! reason: cos(60)=1/2. Another way to come to the conclusion is to construct another angle with 60 degrees from the other corner, which would meet the long side in half. Since the new 60-60-60 triangle has equal sides, it follows the side x is 50.

first looking, i didn't see the line segment... then realized it is an equilateral triangle so x is 1/2 the side...

Both sin(30) and cos(60) finds the right answer, since we can calculate all angles.

@quadmachine8434

4 ай бұрын

But can you calculate any length of the sides with just the angles

@osdboza

4 ай бұрын

@@quadmachine8434 No, but we do have one side of 100 ft, and with that and Sin(30) or Cos(60), we can calculate the distance. And also the polelength using the Pythagoran theorem.

At a glance. Is it 100÷ the cosecant of a 30° angle? That's my first thought... no time spent thinking it through......... am I wrong? I'd love to know if I am....... I realized I picked the wrong offset from center... 30° cosecant not 60° duh...

30,60,90 triangle, ratio 1,2 rt3. X is 1, 100ft is 2.....x = 50ft

It could be interpreted as 0, the wire is touching the pole at the top? But 50 otherwise.

How long did you film this?

I got this right. Where are my stars? 😆

@tonywmckinney

4 ай бұрын

Great vid. Love your channel for refreshing/practicing. Thanks!

When I was in school we called a 30°, 60°, 90° triangle a 3, 4, 5, triangle because this, we were told, was the relationship of the sides in such a triangle. Under that approach, 100ft would would produce a unit measurement of 20ft (100ft ÷ 5 = 20ft). Consequently, 3×20ft=60ft, 4×20ft= 80ft. and 5×20ft=100ft. Unfortunately, this is the first time your explanation and your answer makes no sense to me. Was what I was taught about 3, 4, 5 triangles wrong or has something about 3, 4, 5 triangles changed in 55 years?

@dazartingstall6680

4 ай бұрын

You're correct that 3, 4, 5 is a right triangle, but its angles are 36.87, 53.13, 90 not 30, 60, 90.

B. It's a 30/60/90 triangle, so the short side is half of the hyp.

30, 60, 90 triangle, so short side = 1/2hyp, or 50

@user-ri6rn7ti5h

4 ай бұрын

Yes

I think I like answer (b).

@jimwetzel1635

4 ай бұрын

And, for extra credit, the height of the pole is (100 ft)(sqrt(3)/2) = 86.6 ft, to 3 significant figures.

50 ft

b) 50 ft

b) 50'

Best means of solving is simply to multiply 100 by the cosine of 60 degrees.

@lwh7301

23 күн бұрын

Not everyone remembers what cos 60 is,

@topkatz58

Күн бұрын

​@@lwh7301True but not everyone remembers the 2x, x, x√3 rule either. I forgot it.

b) 50.

Cos(60)x100 ft = 50 ft

x/100 = cos 60 . x= 100 × 1/2 And it took me 50 minutes

100ft × COS(60°) = 50ft

B. 50 feet

Car Accident Help Cos() = Adj / Hyp Adj = Cos() x Hyp Adj = Cos(60) x 100 50 = 0.5 x 100 B Edit - I also use "Take Off Astronaut" and "Sick On Ham" - They are the first ones I thought of and have worked ever since so there was no need to make better ones. That Socatohawhatever is useless. What's the point of a mnemonic if I can't remember how to spell it.

70

Answer is 50 ft

X = 50 ft

The answer is clearly 0 because the wire is tied to the pole at the top. Oh, you meant at ground level, or solve for x. Never mind.

x= 50

This question really isn't valid as shown because it doesn't *state* that the pole is at right angles to the ground or that the wire is pulled straight - or even that it's a flag pole in the ground that's supposed to be vertical (which would make those assumptions reasonable). Plus this is a multi-choice question so there wouldn't normally be a bubble for "assuming the pole is at 90 degrees" to shade in with your 2B pencil. Even the video states "so we have to make the assumption..." yet there's no justification for that in the question beyond "we have to make one of the answers fit somehow". That may be good multi-choice exam technique, but it's not good mathematics (...and that's the problem with over-reliance on multiple choice tests). In other questions it may be very important *not* to get distracted by how the diagram looks - e.g. the "impossible triangle" question on this very channel last week, or the famous "rope between two poles" interview problem (spoiler - the distance between the poles is zero). There's a whole genre of "many will get this wrong" questions which rely on diagrams leading people astray like that. Even when sketching diagrams yourself it's easy to accidentally draw a "special case" and make a mistake. The best rule when dealing with geometry problems is to assume that if an angle or length isn't marked on the diagram then it is unknown. In my experience, geometry questions in important exams often have "not drawn to scale" or "drawn to scale" on such diagrams to make the questions fair. People already struggle enough with mathematics, there's really no need to try and trip them up with trick questions, or sloppy problems with unstated assumptions. Now, if the question *said* that this was a real flagpole, asked you to *estimate* the distance and asked for a written answer - so that they had some clue that they'd need to make simplifying assumptions, and have an opportunity to state them - then you'd have a better question.

A

The pole is correct i.e it is right angled 😂

Cos 60°=1/2sob)50ft is correct.

You’ve so lost me.

50

b) 50 ft