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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

3. 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