# Lesson video

In progress...

Hi, I'm Mrs. Denny.

And in this lesson, we're going to be solving trigonometry problems containing a mixture of finding missing angles, and missing sides.

We're asked to work out the length of the side marked x to one decimal place.

As you can see here, we've got two right angle triangles.

There isn't enough information on the triangle marked x for us to use trigonometry to find the side length.

But if we look at the other triangle, the first triangle, we can see a side and an angle.

And we can use trigonometry to find the height of this triangle.

And this in turn will help us to find x because the height of this triangle corresponds to the height of the second triangle.

So we apply trigonometry to the first triangle.

We have the opposite side length, and we want to find the adjacent side, So we use the tan function.

So we write down tan 47 equals eight over the adjacent or question mark because that's the side that we're looking for.

We rearrange this equation and type in eight divided by tan 47 into our scientific calculators.

We can use this in our second triangle.

So now apply trigonometry to this second triangle, because we've got enough information to do that now.

We need to use the sine function for this one, because we've got the hypotenuse, that's the side that we're trying to find x.

And we've just found the opposite side which is 7.

46, etc.

So we substitute into the sine function, and we using the on rounded height that we found in the first triangle as we want to be as accurate as possible with our answer.

Again, we rearrange this, and we can find x.

So we type that into our calculator and x turns out to be 11.

854, etc.

And we round this to one decimal places.

That's what we're asked to do in the question, and we get 11.

9 centimetres.

Sometimes you may be given a worded problem to solve.

So here we've got a ladder of length eight metres is placed against a wall.

The base of the ladder is 1.

5 metres from the wall.

What is the angle of elevation of the ladder? Give you answer to the nearest degree.

So for this type of problem, it's useful to draw a diagram so that we can visualise what is happening.

So we've got a ladder being placed against a wall and the ladder is eight metres long, and it's placed 1.

5 metres from the wall, we want to find the angle of elevation.

This is the angle formed from looking up from the base of the ladder to the top of the wall, hence the word elevation as we're looking up, and we now have a right-angled triangle with two side lengths, and we're looking for an angle.

So we can use trigonometry to help us to find this angle of elevation.

So we label the triangle with the hypotenuse, opposite and adjacent, we can see that we've got the hypotenuse and adjacent sides of this triangle.

So we have to use the cost function.

And we're going to use inverse cosine because we want to find the angle.

So we type this into our scientific calculator.

Remember to use Shift and Cos for cost to the minus one and then the fraction and we get 79.

19307, etc.

And we round this to the nearest degree as requested.

So that gives us an angle of elevation of 79 degrees.

Here's some questions for you to try.

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

Firstly, we want angle A, B, C.

So we drawing a perpendicular height from B to line AD, splitting the shape into a right angle triangle and a rectangle.

The angle between BC and the perpendicular is 90 degrees.

Work out the rest of the angle between line AB and the perpendicular which has a height of 5.

5 centimetres, the same as line CD.

The difference in the length of the base and the length of the top line is four centimetres.

So this is the length from A to the perpendicular line, we have to use the inverse tan function to find the angle, which is 36 degrees to one decimal place, and then we add on the 90 degrees to the 126 degrees for angle ABC.

We use the same triangle to work out angle BAD.

If you use the side lens four and 5.

5, use tan two minus one our inverse tan.

Again, both the fraction should be inverted as far as now the adjacent and the opposite is now 5.

5.

This gives 54.

0 degrees to one decimal place.

Here's another question for you to try.

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

Split the diagram into two right-angle triangles first and find the horizontal length, which is actually the perpendicular height of the triangles, even though it's on its side.

Use the top triangle first, as there isn't enough information in the bottom triangle to use trigonometry.

We use the cosine function on the first triangle, and then we use the sine function on the second triangle.

Here's a question for you to try.

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

To work out BC, use the tan function.

And then you can either use the Cos function or Pythagoras theorem if you know it, to find the length AC.

Simply add the three side-lengths together to find the perimeter.

Here's a final question for you to try.

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