# The sine and cosine ratios for 30 and 60 degrees

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## Lesson details

### Key learning points

- In this lesson, we will learn how to find missing sides and angles in triangles using sine and cosine for 30 and 60 degrees.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 7 Questions

Q1.

Fill in the gaps: In a right-angled triangle, the ratio of the length of the side adjacent side to the length of the hypotenuse called the ...................

hypotenuse

sine ratio

Q2.

What is the sine ratio of a right angled triangle with angle 30 degrees?

0.2

0.87

Q3.

Which image shows the sides of the triangle correctly labelled (in relation to angle a)?

Option 2

Option 3

Q4.

Complete the following: sine 30 = ..............

cosine 30

sine 60

Q5.

Make y the subject.

Option 1

Option 3

Q6.

b = 14 cm when 𝑥 = ?

15 degrees

30 degrees

Q7.

What is the length of the hypotenuse?

17 cm

4.5 cm

### 7 Questions

Q1.

Complete the statement: In a right angled triangle that has an interior angle of 30 degrees, opposite/ hypotenuse = .................

0.2

0.87

Q2.

Complete the statement: In a right angled triangle that has an interior angle of 60 degrees, opposite/ hypotenuse = .................

0.2

0.5

Q3.

Complete the statement: In a right angled triangle that has an interior angle of 60 degrees, adjacent/ hypotenuse = .................

0.2

0.87

Q4.

Complete the statement: In a right angled triangle that has an interior angle of 30 degrees, adjacent/ hypotenuse = .................

0.2

0.5

Q5.

What is the length of side a?

3.4 cm

6 cm

Q6.

What is the length of side b?

10 cm

3.5 cm

Q7.

What is the size of angle a?

45 degrees

60 degrees