Hey everyone, it's Justin again. In the previous few lessons, you learned about sine,
cosine, and tangent. There's a lot more we can do with these trig ratios so,
let's see what's next. By the end of this lesson, you should be able to apply right triangle
trigonometry to real-world scenarios. Our agenda for this lesson is to work through 2 examples
of figuring out an unknown distance, in the real world, using right triangle trigonometry.
So, what do we mean by using right triangle trigonometry? This means that we'll use the sine,
cosine, and tangent ratios to help us solve for something. And always remember that we're
able to use sine, cosine, and tangent because we're working with right triangles. This little
square in the triangle means this is a right angle and therefore it's a right triangle.
Let's do 2 examples today. Example 1 says: a tree is supported by a wire staked into the ground,
8 feet away from the tree. The acute angle created where the wire meets the ground is 50°. How high
up the tree is the wire attached? We make a picture with a triangle to help us like this.
Don't worry when you're drawing your pictures though, your artistic ability is not for a grade.
Anyways, we can now see that 8 is the side adjacent to the 50° angle;
and the side we don't know, but want to find, is the one opposite to the angle. Since we're
working with the opposite and adjacent sides, we'll be using tangent to help us solve.
Set up an equation knowing that the tangent ratio is the opposite over the
adjacent side. We solve by multiplying both sides by 8. This gives us the exact answer but,
it'll make more sense to find a rounded number. Let's be real, no one's going to know what you
mean when you say that the distance is 8 tangent of 50°. So, we use our calculator
to find a decimal approximation. Let's go ahead and round our answer to the nearest hundredth.
Now it is super important that you're able to get the same answer as me with whatever calculator
you are using. So let's take a time out to look at some calculator tips. First, your calculator needs
to be in degree mode. This is really important for getting the correct solution. Also in degree mode,
you do not need to type the degree symbol. Second tip is that no matter which calculator you use,
if you verify that the tangent of 45° equals 1, then you can be sure that the calculator is
in degree mode and not radian mode. Radians are another way to measure angles but we won't have
to worry about that until pre-calculus. Now that we know more about how to use our calculators,
pause the video and verify that you're able to type in 8 tangent of 50° correctly.
You should get 9.53 as your decimal approximation to the hundredths place.
Great work so far. Let's get back to the original problem. We basically found our answer
but let's just make sure we write it as a sentence. The wire is attached 9.53 feet
up the tree. Our second example says; you are flying a kite directly above your friend's head.
Your friend happens to be 8 feet away from you, and the angle created by a horizontal
line and the kite string is 50 degrees. How much string is being used to fly the kite?
Pause the video here to draw your triangle and try to set up your trig function.
Compare your drawing to what you see here. When you were working on your own did you
figure out that 8 is the adjacent side of the 50° angle? Did you know x was the hypotenuse?
Adjacent and hypotenuse? Ah, this time we need cosine. We have the cosine of 50° equals 8 divided
by x. We multiply both sides of the equation by x and then divide both sides by the cosine of 50°.
Then we can use our calculators to get an answer that will be a lot more useful to us.
Why don't you pause the video one more time and try to figure out the solution.
Let's see how you did. When we round to the hundredths place,
we get that approximately 12.45 feet of string is being used to fly the kite. Well,
that was fun. Now we can apply right triangle trigonometry to real-life scenarios. Did you know
that right triangle trigonometry is even used in marine biology, surveying, video games, and
construction? Remember to watch for those right triangles out there. Maybe you can even think
of a place in your own life where you can use right triangle trigonometry. See you next time.