>> This is Your Math Gal,
Julie Harland.
Please visit my Website
at YourMathGal.com where all
of my videos are organized
by topic.
In this video we're going
to solve this right triangle
that you see right here.
So remember
to solve the right triangle it
means we need
to know all three angles
and all three sides.
So the angles are A, B and C
and the sides are lower case
a, means it's the side
opposite the angle A,
and lower case b
and lower case c. c is the
hypotenuse
because it's opposite the
right angle.
All right, so first of all,
let's write
down what we do know.
We don't know angle A
and we don't know angle B,
so we can't fill anything
in here, but we know angle C
is the 90 degree angle.
All right, do we know side a?
Now the side a is the side
opposite angle A,
and yes we do.
That is 4.1.
Do we know the side opposite
angle B. That's given as 6.2.
And I don't see the decimal
point there.
6.2. And how about side c?
No. Remember,
to solve a right triangle,
first of all you have
to have a right angle,
so you're always going
to know the right angle,
right?
And then you have to have
at least one side.
So in this problem,
we're given two sides.
We don't know either angle
this time.
I can find the third side.
Anytime you have two sides,
one way to find the third side
is just to use the
Pythagorean Theorem.
So remember that if you want
to know the hypotenuse,
which is c,
c squared is the lengths
of the legs squared
and added together.
So it's 6.2 squared plus
4.1 squared.
And so c will just be the
square root of all that.
So just keep in mind
that if you wanted
to know what c was,
you would just take the square
root of it
and that's what you want
to just put
in your calculator.
That would be the exact
answer, whatever you get.
And what we'll do is round
to the nearest 10th.
So in your calculator,
you want to compute the square
root of 6.2 squared plus
4.1 squared.
And when I do that I get 7.4.
Now, notice this is not exact.
It's rounded, okay?
So this is 7.4.
First of all,
it should be longer
than either of the two sides,
and it is.
So that seems
like a reasonable answer.
So we've got 7.4.
Now, so we've got c
figured out.
But I want to use some
of the original information
to figure out a
or b. Be careful.
You don't want
to use something
that you've rounded to find
out something else
because you're going
to get off
because you're going
to have an error.
So you would have left
whatever this was exact,
you could use it.
But if I rounded it,
I don't want to use the 7.4.
So I'm going to try to figure
out how to find angle A
or angle B using these
two sides.
So let's say I wanted
to figure out what angle A is
and I wanted
to use these two sides.
What I'm looking at,
and you know,
from A is the side opposite
and the side adjacent.
So you think,
what trig function uses the
side opposite
and the side adjacent?
And that would be the tangent.
So the tangent
of A would be the side
opposite, 4.1, over 6.2.
Now we don't want
to compute that yet.
That'll tell us what the
tangent of A is.
Now if the tangent
of A is that,
here's where you have
to remember your
inverse functions.
That means
that if A is just the inverse
tangent of that.
So the inverse tangent
of 4.1 over 6.2.
You want to keep everything
exact before you plug it
into your calculator.
This will give us an angle A.
And if you want it in degrees,
make sure that you've got your
calculator set
up in the degree mode.
All right,
so now in your calculator
we're going to plug
in the tan inverse and then
in parentheses 4.1 divided
by 6.2.
And let's round
to the nearest 10th
of a degree.
So you want to put it
in degree mode.
All right, when I do that,
I get that it's approximately
33.5 degrees.
So for A up here,
I have 33.5 degrees.
All right, now I know that A
and B have to add
up to 90 degrees,
so I just do 90 minus 33.5
and now I'm going
to get B 56.5.
You don't have to worry
about starting over
and finding
out B. You could do B
by using the tangent as well.
You could say --
by the way,
let's say somebody wanted
to do that.
Let's just go ahead
and see how
that would have worked.
I know that the tangent
of B would be its opposite,
which is 6.2 over 4.1.
So if I wanted
to know what B is,
I would do the tan inverse
of 6.2 over 4.1.
So go ahead and put
that in your calculator,
the tan inverse
of 6.2 over 4.1.
And hopefully when you rounded
that you did get 56.5 degrees,
all right?
So maybe somebody found
out what B was
and they figured
out A would be a 33.5.
Now we've solved our triangle.
We know all three angles;
we know all three sides.
We see if this makes sense.
Does that look, you know,
approximately correct?
Does like A,
that looks
like the smaller angle,
33.5 and it's
across from the smaller side.
B, the medium size angle is
across from the medium side.
And C, the right angle,
which is the biggest angle,
is across from the largest
side, the hypotenuse.
And if you want,
you could go ahead
and do the Pythagorean Theorem
again, but of course,
that's how we found c
in the first place,
so you can make sure
that 6.2 squared plus 4.1
squared is approximately the
same as 7.4 squared.
All right.
So that's our second problem,
the solving the
right triangle.
This time knowing two sides,
knowing two legs
of a triangle.
This is Your Math Gal,
Julie Harland.
Please visit my Website
at YourMathGal.com where all
of my videos are organized
by topic.