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Find a Missing Side Using the Tan Ratio

In this worksheet, students will use the Tan ratio to find the missing side of a triangle.

'Find a Missing Side Using the Tan Ratio' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Properties and Constructions Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview


Great, this is what we have been waiting for.  Time to top up the tan.


Okay so maybe not that sort of tan.  

We can use the tan ratio, to help us find a missing side length in a right angled triangle.


When we got out to get a tan, we use help in the form of a sun cream formula.

Here, our help is coming from a formula triangle.

tan ratio

T is for tan (which will be given as an angle)

O is for the opposite side from the angle

A  is the adjacent

The line in the middle means divide.


To use this triangle we cover up what side it is we want to find and we are left with a formula to follow.

Who would have thought formulas could be so helpful.

tan ratio

If we want to find the adjacent, cover up the A.  The formula we are left with is opposite ÷ tan(angle)

tan ratio


If we want to find the opposite cover up the O.  The formula we are left with is Tan(angle) x Adjacent.


writing Let's give it a go.


You will need a scientific calculator for this.  Make sure it is set to degrees.


Example 1

tan ratio

1. Label the triangle

2. Find the two sides you want.  You want to find x, so we want O, and the only other side you have to help is the A.

3. Look at your formula triangle, cover up the side you want to find which is O. (see above)

4.  We are left with tan47 x 7

5. In your calculator type in  tan 47 x 7

6. Your answer should be 7.51 cm to 2 decimal places.


Example 2

1. Label your triangle

2. Find the sides you want

3.  You should have discovered you wanted O and A

4. Use your formula triangle and cover up A the side you want to find

5. The formula you are left with is opposite ÷ tan 32 

6. 15 ÷ tan32 = 24.00 cm correct to 2 decimal places


How tantastic is that?

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