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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.

'Find a Missing Angle 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

QUESTION 1 of 10

 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.

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)

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 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 ratio

We want to find the angle, cover up the C.  The formula we are left with is adjacent ÷ hypotenuse

writing 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

cos ratio angle

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.

7. Your answer should be 65.2°  to 1 decimal place.

 

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.

7. Your answer should be 51.3° to 1 decimal place.

 

Clever things these calculators, not geeky after all..but still makes us look good.

 

cos ratio angle

Answer has been rounded to 2 decimal places

35.21°

46.72°

48.19°

39.67°

cos ratio angle

Round your answer to 1 decimal place.

Write your answer in figures without the units.

cos ratio find angles

 

 adjacent x hypotenuseadjacent ÷ hypotenuse63.36°68.68°65.55°
The formula I need is
The angle is

cos ratio

Calculate the size of the angle.

Round your answer to 2 decimal places (2 d.p)

 adjacent x hypotenuseadjacent ÷ hypotenuse63.36°68.68°65.55°
The formula I need is
The angle is

 

cos ratio find angle

Round your answer to 2 decimal places (2 d.p)

22.25°

21.78 °

27.95°

20.69°

cos ratio find angle

Round your answer to 2 decimal places.

Write your answer in figures without the units.

cos ratio find angle

 

 adjacent x hypotenuseadjacent ÷ hypotenuse60°65°55°
The formula I need is
the angle is

Round your answer to 2 decimal places (2 d.p)

 adjacent x hypotenuseadjacent ÷ hypotenuse60°65°55°
The formula I need is
the angle is

cos ratio find angle

Round your answer to 2 decimal places (2 d.p).

Write your answer in figures without the units.

cos ratio angle

Answer has been rounded to 2 decimal places (2 d.p)

48.19°

46.23°

45.67°

47.20°

  • Question 1

 

cos ratio angle

Answer has been rounded to 2 decimal places

CORRECT ANSWER
48.19°
EDDIE SAYS
The tricky part of the question is labelling your triangle correctly. Why do you have to label the triangle? Just be cos.... You should have discovered that you needed the adjacent divided by the hypotenuse. 8 ÷ 12 = 0.6666 cos-1 0.666 = 48.19 (to 2 d.p)
  • Question 2

cos ratio angle

Round your answer to 1 decimal place.

Write your answer in figures without the units.

CORRECT ANSWER
33.6
EDDIE SAYS
How are you going with the labelling of the triangle? It can get tricky I know. Adjacent ÷ hypotenuse 5 ÷ 6 = 0.833 cos-1 0.833 = 33.59 (33.6° to 1 d.p)
  • Question 3

cos ratio find angles

 

CORRECT ANSWER
 adjacent x hypotenuseadjacent ÷ hypotenuse63.36°68.68°65.55°
The formula I need is
The angle is
EDDIE SAYS
Why didn't the sin and tan get on? Just cos... Have you noticed that the formula will always be the same when finding an angle, unlike when trying to find a side. 8 ÷ 22 = 0.3636 Cos-1 0.3636 = 68.68° to 2 decimal places
  • Question 4

cos ratio

Calculate the size of the angle.

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
It is like anything. Once you know the formula, or know how to find it, things become easy as it is just following a set of instructions. 7 ÷ 8 = 0.875 Cos-1 0.875 = 28.96°
  • Question 5

 

cos ratio find angle

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
20.69°
EDDIE SAYS
Are you getting used to this now? It is just a case of keep practicing finding and using the formula. 14.5 ÷ 15.5 = 0.935.. Cos-1 0.935 = 20.69° (2 d.p).
  • Question 6

cos ratio find angle

Round your answer to 2 decimal places.

Write your answer in figures without the units.

CORRECT ANSWER
36.87
EDDIE SAYS
12 ÷ 15 = 0.8 Cos-1 0.8 = 36.87° (to 2 d.p) Top tip. Scientific calculators vary slightly. Make sure you always use the same one so you can get used to their ways.
  • Question 7

cos ratio find angle

 

CORRECT ANSWER
 adjacent x hypotenuseadjacent ÷ hypotenuse60°65°55°
The formula I need is
the angle is
EDDIE SAYS
To be honest once you can label your triangle correctly you can leave the rest to your scientific calculator. What a great friend it is at a time like this. 9 ÷ 18 = 0.5 Cos -1 0.5 = 60°
  • Question 8

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
Calculators are great, they are us look so clever. The only thing you have to be careful of, is rounding to the correct number of decimal places. 2.5 ÷ 6.5 = 0.3846... Cos-1 0.3846... = 67.38° (to 2 d.p)
  • Question 9

cos ratio find angle

Round your answer to 2 decimal places (2 d.p).

Write your answer in figures without the units.

CORRECT ANSWER
63.61
EDDIE SAYS
Nearly there. I hope you haven't found this to tri-ing!! 4 ÷ 9 = 0.444 Cos-1 0.444 = 63.61° (to 2 d.p)
  • Question 10

cos ratio angle

Answer has been rounded to 2 decimal places (2 d.p)

CORRECT ANSWER
48.19°
EDDIE SAYS
And finally, just cos...... You must have been expecting this, a non right angled triangle. What do you do..turn it into a right angled triangle of course. Don't forget to halve the base to get the correct measurement for the adjacent side. 6 ÷ 9 = 0.66666 Cos-1 48.19° (to 2 d.p)
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