Unit 34Pythagoras’ 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

Unit 3434.1 Pythagoras’ Theorem

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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Unit 3434.2 Using Pythagoras’ Theorem

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

Unit 3434.3 Sine, Cosine and Tangent

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

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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Example 2

For the triangle below, what is the value of

(a)

(b)

(c)

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Unit 3434.4 Finding the Lengths of sides

in Right Angled Triangles

Example 1

Find the length of the side marked x in the triangle.Solution

So

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(to 1 d. p.)

Example 2

Find the length of the side marked x in the triangle

Solution

So

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(to 1 d. p.)

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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