Lesson video

Hi.

I'm Miss Davies.

In this lesson we're going to use sine and cosine to find missing length of a right angle triangle.

In this example, we have been asked to calculate the length of the side that is marked X.

Because we have a right angle triangle with two lengths and an angle we're going to use trigonometry.

So, let's start by labelling the sides.

8 cm is our hypotenuse and x is our opposite side.

Because these are the two sides that we are working with we're going to use sine.

Sine of the angle is equal to the opposite divided by the hypotenuse.

If we substitute in the values that we've been given.

This is equal to sin is equal to x divided by 8.

To solve this equation to find X we're going to multiply both sides by 8.

This means that 8 multiplied by sin is equal to x.

We can type 8 multiplied by sin into our calculator and that gives us an answer of x is equal to 6.

71 cm.

This is being rounded 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 8.

66025 which to one decimal place is 8.

7 cm.

In this next example we are being given the length 17 cm and X.

We are being asked to work out the length of the side that is marked X.

Let's start by labelling our triangle.

X is the hypotenuse and 17 cm is our adjacent side.

Because these are the two sides that we're working with we're going to use cosine.

Cos of the angle is equal to the adjacent length divided by the hypotenuse.

If we substitute in the values that we've been given that gives us cos is equal to 17 divided by X.

We need to solve this equation to find the value of X.

Let's start by multiplying both sides by X.

We have to do this because X is the denominator.

This gives us X multiplied by cos is equal to 17.

To solve for X we next need to divide both sides by cos.

This gives us X is equal to 17 divided by cos.

We can then type this into the calculator to get a solution of X is equal to 21.

9 cm correct 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 is exactly 8 cm.

Because sine of 30 is a half.

And 4 divided by half is 8.

Here are some questions for you to try.

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

Here are the answers.

In part A you should have used cosine.

B you should have used sine.

C you should have used sine again.

And in D you should have used cosine.

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.

Cosine should have been used not sine.

Here is a question for you to try.

Drawing out a diagram might help you answer this question.

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 1.

6 divided by cos which gives an answer of 3.

2 m.

That's all for this lesson.