Lesson video

Hi, I'm Miss Davies, in this lesson, we're going to be using tangent to find a missing length of a right-angled triangle.

We're been asked to calculate the length of the side marked x.

Because we have got one side, an unknown side and an angle, we're going to have to use trigonometry.

Let's start by labelling our triangle.

We have got the adjacent side and the opposite as our unknown.

This means that we're going to use tangent.

Tangent of the angle is equal to the opposite length divided by the adjacent length.

We substitute in our values that gives us tan of 40 is equal to x over 15.

To solve this equation for x, we're going to multiply both sides by 15.

15 multiplied by tan of 40 is equal to the missing length x.

If we type this into our calculator, it gives us 12.

6 centimetres to three significant figures.

Here is a question for you to try, pause the video to complete your task, and resume once you're finished.

Here are the answers.

Your final answer, should have been 7.

002 which rounds to 7.

0 centimetres to one decimal place.

In this next example, we have been asked to find the length of the side marked x let's start by labelling our triangle again, we have got our adjacent and opposite lengths so we're going to be working with tangent.

Tan of the angle is equal to the opposite length divided by the adjacent length.

If we substitute in the values that we've been given that gives us tan of 57 is equal to eight divided by x.

We need to solve this equation, to find the length x the first thing we're going to do is multiply both sides by x.

This gives us x multiplied by tan of 57 is equal to eight.

To get x on its own, we're going to divide both sides by tan 57.

X is equal to eight divided by tan 57.

If we type this into our calculator, it gives us a solution of 5.

2 centimetres to one decimal place.

Here is a question for you to try, pause the video to complete your task, and resume once you're finished.

Here are the answers.

Your final answer should have been 0.

1212 which to two decimal places is 0.

12 metres.

Here is some questions for you to try, pause the video to complete your task, and resume once you're finished.

Here are the answers.

For all of these questions you should have rounded your answer to three significant figures if you have rounded your answer to something slightly different such as one decimal place, and you've got a slightly different answer, your working out will still be correct.

Here is a question for you to try, pause the video to complete your task, and resume once you're finished.

Here is the answer.

Lycia has multiplied by 63 but she should have multiplied by AB and then divided by 63.

You can only multiply by the denominator of a fraction.

Here is a question for you to try, draw out a diagram to help you answer it.

pause the video to complete your task, and resume once you're finished.

Here is the answer.

The calculation that you should have typed into your calculator is three multiplied by tan 60.

This gives you an answer of 5.

196 which rounds to 5.

2 metres.

That's all for this lesson, thanks for watching.