  # Find a Missing Angle Using the Cos Ratio

In this worksheet, students will use the Cos ratio to find the missing angle of a right angled triangle. 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 Did you know that the word trigonometry came from the ancient Greeks.  'Trigonon' was their word for triangle and 'metron' their word for measure.

Don't you think these ancient Greeks were a bit geeky? I like being a maths geek.  People think I am really clever, but it is just a case of using formulas that the ancient Greeks gave us years ago... makes us look good.

(SOH, CAH, TOA) yes that again.

We are going to look at Cos here.

We can use Cos to help us find the missing angles 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)

H is the hypotenuse

The line in the middle means divide. To use this triangle we cover up what it is we want to find and we are left with a formula to follow.

Who would have thought formulas could be so helpful. We want to find the angle, cover up the C.  The formula we are left with is adjacent ÷ hypotenuse Let's give it a go.

IMPORTANT NOTE:  Make sure your calculator is set to degrees.  You should see a D in your window.

Example 1 1. Label the triangle

2. Find the two sides you want.

You want to find the angle, so we want A, and the only other side you have to help is the H.

3. Look at your formula triangle, cover up C

4.  We are left with Adjacent ÷ Hypotenuse

5. In your calculator type in  3 ÷ 7 = 0.42 (This is clearly wrong)

This is the geeky bit

6. Type into your calculator Shift Cos to access Cos-1  0.42 which will give us the angle.

Example 2 1. Label the triangle

2. Look at your formula triangle, cover up C

4.  We are left with Adjacent ÷ Hypotenuse

5. In your calculator type in  5 ÷ 8 = 0.625

6. Do the geeky bit Shift Cos to access Cos-1  0.625 which will give us the angle. 