Lesson video

Hi.

I'm Mrs. Dennett.

And in this lesson, we're going to be substituting exact values for trigonometric ratios into equations to find a missing length.

So before you start this lesson, you'll need to have learned about exact values for sin, cos, and tan before you start.

You should have learned about how to find these values using an equilateral triangle and a right angled isosceles triangle.

And it will be useful to recap how to draw these triangles before we start.

So we're going to work out the size of the length of marked X, without using a calculator.

So we're going to be using trigonometry 'cause we've got side and angle.

So that's good.

And we've got a right angle triangle, very important.

So we label our right angle triangle, and we can see that we've got the opposite side.

And we're trying to find the hypotenuse.

So this tells us that we're going to be using the sin ratio.

So we substitute the values that we've got into our sin ratio to get sin 30 equals seven divided by X.

Now at this point, we need to know the exact value for sin 30.

You may have already learned some of these, or you might want to check in a table or you might want to draw one of the two triangles that you've looked at previously to help you to find the exact values of sin, cosine, tan for different angles.

So what we can do is we're just going to use our table, and we can look and find that sin 30 is equal to 1/2.

So we write that down.

1/2 equals seven divided by X.

And this tells us that X must be 14 centimetres.

Let's try another question.

So here we want to work out the size of the missing length X without using a calculator.

So we label our triangle, and we've got the opposite and the adjacent side.

So we're trying to find the opposite, and we've got the adjacent side is 11 centimetres.

And we've also got our angle.

So we know that we're going to be using the tan ratio.

Tan 60 is equal to X divided by 11.

So what we need to do now is find out the value of tan 60.

So we can do this using our table, or we can draw an equilateral triangle so that we get a value of 60 degrees and half it.

Find the missing side lengths and then find tan 60.

I'm going to use the table because it's a little bit quicker.

So we've got the tan 60 is equal to root three.

So we rewrite our equation as root three equals X divided by 11.

And then we have to multiply both sides of the equation by 11.

So we get X is equal to 11, root three centimetres.

Here are some questions for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers.

For part A, you need to know that sin 30 is equal to 1/2.

In part B, we use the fact that tan 45 is equal to one.

For C, we need cos 60 equals 1/2.

And finally for part D, use cos 30 equals root three over two.

Here's a question for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

In this question, we have to apply trigonometry to each triangle in turn as there isn't too much information to find extra straightaway.

So use the top triangle to find the horizontal perpendicular height, which is seven root three since cos 30 is equal to root three over two.

And then find X using sin 30 equals 1/2.

So X must be double seven, root three, which is 14 root three.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.