# Trigonometric Ratios

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

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Difficulty level:

### 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 ?

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 ?

4/5
• Question 2

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

4/3
• Question 3

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

3/4
• Question 4

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

3/5
• Question 5

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

4/5
• Question 6

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

5/13
• Question 7

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

12/13
• Question 8

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

5/12
• Question 9

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

5/13
• Question 10

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

12/5
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