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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
Unit 34
34.1 Pythagoras’ Theorem
Pythagoras’ theorem states that for any right angled triangle.
2
ExampleExample
1
the length
of side
x.
What is Find
the length
of a (the
hypotenuse)?
SolutionSolution
??
?
?
?
??
?
?
?
?
?
?
?
?
?
Unit 34
34.2 Using Pythagoras’ Theorem
Here we see how Pythagoras’ Theorem can be used to solve
different problems.
D
Example 12
Find the length
ofxthe
marked
value of
as side
shown
in thex
in
the diagram.
diagram,
giving the lengths of the two
unknown sides
Solution
In triangle ABC
Solution
?
?
??
?
C
Pythagoras’ Theorem gives
In triangle ACD
?
?
?
?
So?
?
?
?
A
?
?
?
?
? ?
?
B
Unit 34
34.3 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
(b) Adjacent
(c) Opposite
?
CB
?
AC
AB
?
Example 2
For the triangle below, what is the
value of
?
(a)
?
?
?
(b)
?
?
(c)
?
?
?
Unit 34
34.4 Finding the Lengths of sides
in Right Angled Triangles
Example 1
Find the length of the side marked x
in the triangle.
Solution
So
?
?
?
?
?
(to 1 d. p.)
Example 2
Find the length of the side marked x
in the triangle
Solution
So
?
?
?
?
?
(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)
?
?
?
?
?