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Trigonometric Ratios

In this worksheet, student work out the given trigonometric ratio in right-angled triangles.

'Trigonometric Ratios' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In a right-angled triangle, the sides and the angles are connected by three trigonometric ratios.

 

 

The three trig ratios are:

 

 

A quick way to remember this is to memorise the word

SOHCAHTOA

 

Example

Use the side lengths of this triangle to state the value of cosθº ?

 

 

Answer

Label the sides adjacent, opposite and hypotenuse in relation to the angle θº.

 

 

SOHCAHTOA

 

The side adjacent to the angle θ has length 3.

The hypotenuse has length 5.

 

The correct trig ratio is COS so cos θº= 3/5

 

Use the side lengths of this triangle to state the value of sinθº ?

 

3/5

4/5

3/4

5/3

5/4

4/3

Use the side lengths of this triangle to state the value of tanθº ?

 

3/5

4/5

3/4

5/3

5/4

4/3

Use the side lengths of this triangle to state the value of tanβº ?

 

3/5

4/5

3/4

5/3

5/4

4/3

Use the side lengths of this triangle to state the value of sinβº ?

 

3/5

4/5

3/4

5/3

5/4

4/3

Use the side lengths of this triangle to state the value of cosβº ?

 

3/5

4/5

3/4

5/3

5/4

4/3

Use the side lengths of this triangle to state the value of sinθº ?

 

5/12

5/13

12/13

13/12

13/5

12/5

Use the side lengths of this triangle to state the value of cosθº ?

 

5/12

5/13

12/13

13/12

13/5

12/5

Use the side lengths of this triangle to state the value of tanθº ?

 

5/12

5/13

12/13

13/12

13/5

12/5

Use the side lengths of this triangle to state the value of cosβº ?

 

5/12

5/13

12/13

13/12

13/5

12/5

Use the side lengths of this triangle to state the value of tanβº ?

 

5/12

5/13

12/13

13/12

13/5

12/5

  • Question 1

Use the side lengths of this triangle to state the value of sinθº ?

 

CORRECT ANSWER
4/5
  • Question 2

Use the side lengths of this triangle to state the value of tanθº ?

 

CORRECT ANSWER
4/3
  • Question 3

Use the side lengths of this triangle to state the value of tanβº ?

 

CORRECT ANSWER
3/4
  • Question 4

Use the side lengths of this triangle to state the value of sinβº ?

 

CORRECT ANSWER
3/5
  • Question 5

Use the side lengths of this triangle to state the value of cosβº ?

 

CORRECT ANSWER
4/5
  • Question 6

Use the side lengths of this triangle to state the value of sinθº ?

 

CORRECT ANSWER
5/13
  • Question 7

Use the side lengths of this triangle to state the value of cosθº ?

 

CORRECT ANSWER
12/13
  • Question 8

Use the side lengths of this triangle to state the value of tanθº ?

 

CORRECT ANSWER
5/12
  • Question 9

Use the side lengths of this triangle to state the value of cosβº ?

 

CORRECT ANSWER
5/13
  • Question 10

Use the side lengths of this triangle to state the value of tanβº ?

 

CORRECT ANSWER
12/5
---- OR ----

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