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Examples and explanations of how to use the Pythagorean Theorem and trigonometric functions to find missing sides and angles in right triangles. It includes step-by-step solutions for various problems and the use of trigonometric ratios such as sine, cosine, and tangent.
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Lesson 9- 1
2
2
2
2
2
2
Note: Pythagorean Theorem is only use in RIGHT TRIANGLES
to find one missing side.
Missing side =
Find the missing side of the right triangle.
x
14
7
SOLUTION
2 2
(hypothenuse) -(givenside)
Missing Side =
2 2
(hypothenuse) - (given side)
x =
2 2
x =
x =
x =
THE PYTHAGOREAN THEOREM
THE PYTHAGOREAN THEOREM
Missing Side =
2 2
(hypothenuse) - (given side)
x =
2 2
x =
x =
(^) x ≈ 15.492 Answer: D
CONVERSE OF THE PYTHAGOREAN THEOREM
Converse of the Pythagorean Theorem
If c
2
=
a
2
2
then ∆ ABC is a right ∆
CLASSIFYING TRIANGLE THEOREM
If c
2
<
a
2
2
then ∆ ABC is an acute ∆
CLASSIFYING TRIANGLE THEOREM
Example
Decide whether the set of numbers can represent the
side lengths of a triangle. If they can, classify the
triangle as right , acute , or obtuse.
Lesson 9-4, 9- 5
Thursday, April 9, 2020
Example 2) In the right triangle identify the hypotenuse, opposite
side and adjacent side of angle B
side and adjacent side of angle
Example
a
b
c
WHAT IS TRIGONOMETRY?
Trigonometry is the study of how the
sides and angles of a triangle are
related to each other.
Trigonometric Ratio
The six trigonometric function are abbreviated as
follows;
sin θ=
opp
hyp
cos θ=
adj
hyp
tan θ=
opp
adj
3 main Trigonometric Functions
csc θ =
hyp
opp
sec θ =
hyp
adj
cot θ =
adj
opp
Reciprocal Trigonometric Functions
To easily remember the 3 main Trigonometric Functions
EVALUATING TRIGONOMETRIC FUNCTIONS
sin A=
tan A=
cot A (^) =
Angles that deserve special study are 30
º
º
, and 60
º
sin 30
0
cos 30
0
tan 30
0
csc 30
0
sec 30
0
cot 30
0
sin 60
0
cos 60
0
tan 60
0
csc 60
0
sec 60
0
cot 60
0
Angles that deserve special study are 30
º
º
, and 60
º
TRIGONOMETRIC FUNCTIONS OF SPECIAL ANGLES
sin 45
0
cos 45
0
tan 45
0
csc 45
0
sec 45
0
cot 45
0