Lesson video

Hi, I'm Mrs. Dennett.

And in this lesson, we're going to be applying our prior knowledge of Pythagoras and Trigonometry, to help us decide on the most appropriate method to use to solve some problems. In this question were asked, whether we would use Pythagoras or Trigonometry to work out X.

X is a side length.

So we're also given two other side lengths.

If we want to use Pythagoras to work out a side length, we need two other side length in order to do this.

So it makes sense in this question that we would use Pythagoras.

We couldn't use Trigonometry here because even though we want to work at a side length and Trigonometry can help us to do that, we need another angle to help us.

So we've got the right angle, which tells us that it's a right angle triangle, and we can use Trigonometry, but we would need an angle and at least one side length to help us, to find the missing length X using Trigonometry.

So now that we know that we're going to use Pythagoras, let's work out X.

Pythagoras tells us that we have to square the shorter sides, add them together, and that gives us the square of the longer side.

So here we've got 12 squared, plus X squared, equals 19 squared 'cause 19 is the longest side, the hypotenuse.

So we works out and we find that X squared is 217, when we rearrange.

So X is 14.

7 centimetres.

So here we have another question, and in this right angle triangle, we are given a side length 12 centimetres, an angle of 27 degrees, and we've got L side length X that we want to find.

So for this question, we can't use Pythagoras because Pythagoras requires at least two side lengths in order to find a missing side length.

For Trigonometry, we need an angle under side length, which we have got 12 centimetres and 27 degrees.

So in this question, we would use Trigonometry to work out the missing side length X.

So let's work out X.

So we label our triangle and we can see that we've got the opposite and the adjacent sides.

This tells us that we're going to be using the tan ratio.

So we write down tan 27 equals X divided by 12.

And we rearrange that to find X.

So X is 6.

11 centimetres.

Let's have a look at a question where we're given a right angle triangle, and we want to work out a missing angle.

Pythagoras doesn't allow us to work out missing angles.

It would only help us to work out our missing side length.

And we don't want that here.

So we have to use Trigonometry.

So we check that we've got right angle triangle because Trigonometry works for right angle triangles, and we've got two side lengths and we're finding an angle so we can work out the missing angle X, using the two side lengths that we've been given.

So we're going to use Trigonometry to find out angle X and we're going to work out now.

So we label our triangle and we've got the adjacent and hypotenuse in terms of side lengths.

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

So we substitute the values that we've got into our cos ratio.

And we get cos X, which is the angle equals eight divided by 19.

And we're going to have to use cos to the minus one or inverse cos to help us to find the missing angle.

So we type into our calculator, cos to minus one of eight divided by 19, and that gives us 65.

1 degrees for our missing angle.

Here's some questions for you to try.

All you have to do is decide whether you would use Pythagoras or Trigonometry.

Pause the video now to have a go at these questions and restart when you are finished.

Here are the answers, for part A, We have an angle and a side length given, so we use Trigonometry.

In part B, we could use Pythagoras using the two side lengths, or we could use Trigonometry using the angle on one of the side lengths.

For part C, we've got two side lengths, so we have to use Pythagoras.

And for part D, we're finding an angle, so we have to use Trigonometry.

Here's some questions for you to try.

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

Here are the answers.

For part A, use Trigonometry and the sine ratio.

For part B, we use Trigonometry again, but this time use the tan ratio.

The C, we use Pythagoras or Trigonometry.

And for D, we have to use Pythagoras.

Here's a question for you to try.

Pause the videos to complete the task and restart when you were finished.

Here's the answer.

We have to use Trigonometry first to find the perpendicular height of the triangle, which is 6.

71 centimetres.

And then use this side and 3.

5 centimetres with Pythagoras to get X equals 7.

6 centimetres.

Here's a final question for you to have a go at.

Pause the video to complete the question and restart when you were finished.

Here's the answer.

We have to split the trapezium into a rectangle and a right angled triangle first, work out the base length of the triangle, which is eight centimetres.

Use the cos ratio to find the hypotenuse, which is also the slope in length of the trapezium, and then use the tan ratio to find the opposite side, which is also the height of the trapezium.

You could use Pythagoras at this point if you wanted.

You should get 12.

7 and 9.

9 when rounded and these add to 12 and four to get the perimeter.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.