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Pythagorean Theorem and Trigonometry: Finding Missing Sides and Angles in Right Triangles, Study notes of Trigonometry

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.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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RIGHT TRIANGLE &
TRIGONOMETRY
-Pythagorean Theorem
-Converse of the Pythagorean Theorem
Lesson 9-1
Thursday, April 9, 2020
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Download Pythagorean Theorem and Trigonometry: Finding Missing Sides and Angles in Right Triangles and more Study notes Trigonometry in PDF only on Docsity!

RIGHT TRIANGLE &

TRIGONOMETRY

  • Pythagorean Theorem
  • Converse of the Pythagorean Theorem

Lesson 9- 1

Thursday, April 9, 2020

THE PYTHAGOREAN THEOREM

The Pythagorean Theorem

In a right triangle, the square of the length of the

hypotenuse is equal to the sum of the squares of

the lengths of the two sides.

c

a

b

c

2

a

2

+ b

2

z

x

y

z

2

x

2

+ y

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 the square of the length of the longest side

of a triangle is equal to the sum of the squares

of the lengths of the other two sides, then the

triangle is a right triangle.

c

a

b

If c

2

=

a

2

  • b

2

then ∆ ABC is a right ∆

CLASSIFYING TRIANGLE THEOREM

Theorem 7.3 Acute Triangle Theorem

If the square of the length of the longest side of a

triangle is less than the sum of the squares of

the lengths of the other two sides, then the

triangle is an acute triangle.

If c

2

<

a

2

  • b

2

then ∆ ABC is an acute ∆

c

a

b

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.

RIGHT TRIANGLE &

TRIGONOMETRY

  • What is Trigonometry
  • Trigonometric Ratio

Lesson 9-4, 9- 5

Thursday, April 9, 2020

ANGLE AND SIDE RELATIONSHIP OF A RIGHT TRIANGLE

Example 2) In the right triangle identify the hypotenuse, opposite

side and adjacent side of angle B

A

B

x

y

hypotenuse = z

Opposite side of angle B = y

Adjacent side of angle B = x

  1. In the right triangle identify the hypotenuse, opposite

side and adjacent side of angle 

Example

a

b

c

hypotenuse = c

Opposite side of angle  = a

Adjacent side of angle  = b

WHAT IS TRIGONOMETRY?

Trigonometry is the study of how the

sides and angles of a triangle are

related to each other.

Trigonometric Ratio

A trigonometric ratio is a ratio of the

lengths of two sides in a right triangle

THE SIX 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

“SOH-CAH-TOA”

EVALUATING TRIGONOMETRIC FUNCTIONS

Example 1: Find the values of the six

trigonometric functions of angle A in the right

triangle.

sin A=

cos A

tan A=

csc A

sec A

cot A (^) =

 Angles that deserve special study are 30

º

º

, and 60

º

TRIGONOMETRIC FUNCTIONS OF SPECIAL RIGHT TRIANGLE

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