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1. Unit 34
Pythagoras’ Theorem and
Trigonometric Ratios
Presentation 1 Pythagoras’ Theorem
Presentation 2 Using Pythagoras’ Theorem
Presentation 3 Sine, Cosine and Tangent Ratios
Presentation 4 Finding the Lengths of Sides in Right Angled Triangles

2. Unit 34
34.1 Pythagoras’ Theorem

3. Pythagoras’ theorem states that for any right angled triangle.
Example 1
What is the length of a (the hypotenuse)?
Solution
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Example 2
Find the length of side x.
Solution
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4. Unit 34
34.2 Using Pythagoras’ Theorem

5. Example 1
Find the length of the side marked x
in the diagram.
Solution
In triangle ABC
In triangle ACD
Example 2
Find the value of x as shown in the
diagram, giving the lengths of the two
unknown sides
Solution
Pythagoras’ Theorem gives
So
Here we see how Pythagoras’ Theorem can be used to solve
different problems.
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C
BA
D

6. Unit 34
34.3 Sine, Cosine and Tangent

7. For a right angled triangle, the
sine, cosine and tangent of the
angle θ are defined as:

8. Example 1
For the triangle and angle θ
state which side is
(a)Hypotenuse CB
(b)Adjacent AC
(c)Opposite AB
?
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?

9. Example 2
For the triangle below, what is the
value of
(a)
(b)
(c)
?
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10. Unit 34
34.4 Finding the Lengths of sides
in Right Angled Triangles

11. Example 1
Find the length of the side marked x
in the triangle.
Solution
So
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(to 1 d. p.)

12. Example 2
Find the length of the side marked x
in the triangle
Solution
So
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??
(to 1 d. p.)

13. Example 3
For the diagram
calculate to 3
significant figures
(a) The length of FI
(b) The length of EI
(c) The area of EFGH
Solution
(a)
(b)
(c)
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