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Find a Missing Angle Using the Tan Ratio

In this worksheet, students will use the Tan ratio to find an angle of a right angled triangle.

'Find a Missing Angle 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:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview

sun cream and sun glasses


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

Okay, so you have to learn your trigonometry ratio first.  

We can use the tan ratio, to help us find an angle in a right-angled triangle.


Here, our help is coming from our 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 to divide.


To use this triangle we cover tan(the angle we want to find) and we are left with a formula to follow.

tan ratio angle

  The formula we are left with is opposite ÷ adjacent.




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

Example 1


1. Label the triangle

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

3. Look at your formula triangle, cover up the T (the angle)  (see above)

4.  We are left with opposite ÷ adjacent

5. In your calculator type in  6 ÷ 5 = 1.2

6. To turn your 1.2 into an angle you need to access the tan-1 button on your calculator. Do this by pressing shift, then tan.

7. tan-1  1.2 = 50.2° correct to 1 decimal place.


Example 2

tan ratio find an angle

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 angle you want to find

5. The formula you are left with is opposite ÷ adjacent

6. 3 ÷ 2 = 1.5

7. Do the geeky bit, tan-1 1.5 = 56.3° to 1 decimal place.


How tantastic is that?

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