Acute Right and Obtuse Angles

In this video, I
really just want

to introduce you
to some terminology

for some basic angle types.

And the terminology I
want to introduce you to

are acute angles, right
angles, and obtuse angles.

And I think when we
just go through these,

they'll be pretty
self-explanatory.

An acute angle is an
angle-- well, let me just

draw them first.

Then it might start
to make sense.

So an acute angle will
look something like that.

I draw two rays that are
coming from a common point.

So the acute angle will be
this angle right over here.

I could also draw an
acute angle, maybe

an angle that's formed from
the intersection of two lines.

This angle will be acute,
and so will this angle.

They're both acute angles.

And we're going to see is
acute angles are ones that

are-- since I haven't defined
right angles yet-- they're

narrower.

And what we're going
to see is that they're

smaller than right angles.

Right angles are when the
rays or the lines are going,

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

in my definition-- but if
one is going horizontal,

the other one will
be going vertical.

So let me draw it
with the rays first.

So the right angle, this
one's going from the left

to the right.

Then 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, as a traditional angle.

But the general convention
for labeling right angles

is to put a little, kind of a
half of a box right over there.

And that means that
is a right angle.

Or that if this is
going left to right,

this is going perfectly
top to bottom,

that this is in no way kind of--
I guess the best way to think

about it and why
it's called right

is that this ray is
completely upright, compared

to this ray over here.

And let me draw it
with some lines.

So if I have one line
like this and then 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 was the ground,

this line is completely
upright, relative to this line

over here.

So either of these, that's
what a right angle means.

And now that we've
defined right angle,

I can give you another
definition for an acute angle.

An acute angle has a
measure, or it's smaller,

than a right angle.

When you learn about
radians and degrees, which

are different ways
to measure angles,

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, its opening
is smaller, it's more narrow,

the lines are-- you would
have to rotate one line less

to get to the other line
than you would over here.

Here, you'd have to move
it all the way over there.

Here, you'd only have
to move it a little bit.

So the acute angle is
less than a right angle.

And 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 make it a little bit clearer.

It might look like that.

If this was a right
angle, this line over here

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.

And 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.

So you could imagine this looks
like a sharp point or it's not

opening up much, so maybe
it's more sensitive relative

to other things,
or I don't know.

I'm 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
because I don't know.

Maybe that's 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 if you measure it.

You would have to
rotate this ray more

to get to this other ray
than you would if they were

right angles, and
definitely a lot more than

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've drawn
them right over here,

these two over here are acute,
and then these over here

are going to be obtuse.

This one and this one, these
are both obtuse angles.

And I actually drew
it up here, as well.

This one and this one
are going to be obtuse.

So very simple idea.

If one line or one ray
relative to the other one

is straight up and down,
versus to left and right,

or is completely
upright, then we're

talking about a right angle.

If they're closer to
each other, if you

have to rotate them less, you're
talking about an acute angle.

If you have to rotate
them more, you're

talking about an obtuse angle.

And I think when you just
look at them visually,

it's pretty easy to pick out.