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Find a Missing Side Using the Cos Ratio

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

'Find a Missing Side Using the Cos Ratio' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview

 Its all Greek to me

greek flag

Did you know that the word trigonometry came from the ancient Greeks.  'Trigonon' was their word for triangle and 'metron' their word for measure.

Cool stuff how all this history comes into our maths.

Trigonometry - measuring triangles, sounds simple then.



 (SOH, CAH, TOA) is something that every maths teacher has probably chanted at you.

We are going to look at Cos here.  

We can use Cos to help us find the missing side in a  right angled triangle.

A formula triangle is helpful.  The stuff in the triangle is going to help us.

C is for Cos (which will be given as an angle)

A is for adjacent  angle

H is the hypotenuse

The line in the middle means divide.

cos formula triangle


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.

cos formula triangle

If we want to find the adjacent side, cover up the A.  The formula we are left with is Cos(angle) x Hypotenuse.


If we want to find the hypotenuse, cover up the H.  The formula we are left with is adjacent (A) divided by Cos(angle)


writing Let's give it a go.

IMPORTANT NOTE:  Make sure your calculator is set to degrees.  You should see a D at the top of the screen.

Example 1

1. Label the triangle

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

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

4.  We are left with cos47 x 7

5. In your calculator type in  cos 47 x 7

6. Your answer should be 4.77 cm to 2 decimal places.

Example 2

1. Label your triangle

2. Find the sides you want

3.  You should have discovered you wanted H and A

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

5. The formula you are left with is adjacent ÷ cos x 10

6. 15 ÷ cos32 = 17.69 cm correct to 2 decimal places


Greek doesn't seem so bad after all

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