Upload
elearningja
View
188
Download
2
Embed Size (px)
Citation preview
Unit 34Pythagoras’ Theorem and
Trigonometric Ratios
Presentation 1 Pythagoras’ TheoremPresentation 2 Using Pythagoras’ TheoremPresentation 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 1What is the length of a (the hypotenuse)?Solution
??
?
??
??
Example 2Find the length of side x.Solution
?
?
??
??
?
?
?
Unit 3434.2 Using Pythagoras’ Theorem
Example 1Find the length of the side marked x in the diagram.SolutionIn triangle ABC
In triangle ACD
Example 2Find the value of x as shown in the diagram, giving the lengths of the two unknown sides
SolutionPythagoras’ Theorem gives
So
Here we see how Pythagoras’ Theorem can be used to solve different problems.
?
??
???
??
?
?
?
??
?
??
?
?
?
?
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 1For the triangle and angle θ state which side is(a)Hypotenuse CB(b)Adjacent AC(c)Opposite AB
?
?
?
Example 2For the triangle below, what is the value of
(a)
(b)
(c)
?
?
?
?
?
?
?
?
?
Unit 3434.4 Finding the Lengths of sides
in Right Angled Triangles
Example 1Find the length of the side marked x in the triangle.Solution
So
?
??
??
(to 1 d. p.)
Example 2Find the length of the side marked x in the triangle
Solution
So
?
??
??
(to 1 d. p.)
Example 3For 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)
?
?
?
?
?
?
?
?
? ?
?