Acute Right and Obtuse Angles

The difference between acute, obtuse and right angles

In this video, I really wanted to introduce

you to some terminology for some basic angle types

and terminology. I wanted to introduce you to are

acute angles, right angles, and obtuse angles.

I think when we go through these,

it will be pretty self-explanatory.

And an acute angle is an angle --

let me just draw them first

then you might,

you might,

it might start to make sense.

So an acute angle

will look something like that.

I draw two rays

coming from a common point.

I could also --

so the acute angle could be this angle right over here.

I could also draw an acute angle;

maybe an angle that is formed from an intersection of two lines,

so this angle would be acute,

and so will this angle.

They're both acute angles.

We are going to see acute angles as ones

that are --

that since I haven't defined right angles yet.

They are narrower,

so we are going to see that they are

smaller than right angles.

Right angles are when the rays

or the lines are going, oh

I guess, I don't want to use the word "right"

in my definition.

They are kind of

if one is going horizontal

then the other one will be going vertical.

so let me draw with rays first

so the right angle

this one is going from the left to the right

and the other ray is going from the bottom

to the top

this angle right over here

is a right angle

and I could label it like that

but as a traditional angle

but the general,

the general convention for labeling right angles

is to put a little,

a kind of a half of a box over there.

That tells me that this is a right angle

or, that if this is going left to right

this is going perfectly top to bottom

that this is a no way kind of

that this is a completely,

I guess the best way to think about it

why it's called right

is that this ray is completely upright

compared to this ray over here

let me draw with some lines

if I have one line like this

and I have another line like that

a right angle over here

actually all of these would have to be

right angles

it would mean that this line

is completely,

if this line were the ground,

this line is completely upright

relative to this line over here.

so either these,

so that is what a right angle means

so now that we defined right angle

I can give you another definition for acute angle

so an acute angle has a measure

or it's smaller than a right angle

so you learn about radients and degrees

which are different ways to measure angles

so you'll see that a right angle

can be measured as 90 degrees

this over here is less than 90 degrees

so this is less than 90 degrees.

and one way to conceptualize this is

that this angle,

it's opening is smaller

it's more narrow,

it's lines are,

you would have to rotate one line

less to get to the other line

then you would over here.

here, you would have to move

all the way over there

here you only have to move it a little bit

so the acute angle is less than a right angle

so you might imagine already

what an obtuse angle is

it is greater than a right angle

so let me draw a couple of examples

of obtuse angles

so an obtuse angle might look like

let me get it a little clearer

might look like that

if it was a right angle,

then this line over here

would be,

would look something like that

it would be completely upright

relative to this, if this were the ground.

but we don't see that

this orange ray over here is actually

opened out wider

it's opened up wider

so it is obtuse.

it is obtuse

so this kind of comes from the actual

everyday meaning

acute means very sharp or very sensitive

obtuse means not very sharp or not very sensitive.

you could imagine this looks like a sharp point

or it's, it's not opening up much.

so maybe it's more sensitive to

you know, relative to other things

I don't know, just trying to make connections

This is less sensitive

It's all big and open

It won't be able to notice things that are small

or maybe that is not an appropriate analogy

but one way to think about it

it's kind of open up wider,

or it's bigger than a right angle

it's larger than 90 degrees

larger than 90 degrees

if you measure it

you would have to rotate this ray more to

get to this other ray

than you would if you had right angles

and definitively a lot more if they were acute angles.

If I were to draw this with lines,

which of the angles are obtuse and

which are acute?

Well the way I drawn them right over here,

these two over here are acute

are acute

and then these over here are going to be

obtuse

so this one

and this one

these are both obtuse angles

and I actually drew them up here as well.

This one and this one are going to be

obtuse

so very simple idea

if one line

or if one ray is relative to the other one

is straight up and down

versus left to the right

or is completely upright

then we're talking about a right angle

if they are closer to each other

if you had to rotate them less

you're talking about a acute angle

if you had to rotate them more

you are talking about an obtuse angle

and I think if you look at them visually

it's pretty easy to pick out