# Finding missing sides using sine and cosine for any angle

# Finding missing sides using sine and cosine for any angle

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## Lesson details

### Key learning points

- In this lesson, we will learn how to find missing sides using sine and cosine for any angle in a triangle.

### 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.

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

### 7 Questions

Q1.

What is the length of side marked q ?

10 cm

5 cm

Q2.

What is the length of the side marked r ?

15 cm

22 cm

Q3.

What is the correct step for calculating the length of side b?

Option 2

Option 3

Q4.

What is the length of of b correct to 1 decimal place?

0.86 cm

10 cm

Q5.

What is the correct step for calculating the length of side a?

Option 1

Option 2

Q6.

What is the length of a, correct to 1 decimal place?

0.5 cm

23 cm

39.2 cm

Q7.

Which ratio would you use to find the length of the missing side in the triangle below?

pythagoras

sine