student book

NURWAHIDAH

(091104184) INTERNATIONAL CLASS

PROGRAM OF MATHEMATICS

2009

BASIC COMPETENCE

BASIC COMPETENCE

Using Pythagorean Theorem to determine the length of right triangle

In this chapter, you will:

• Discover the

Pythagorean

Theorem.

• Use the Pythagorean

Theorem to calculate

the distance between

any two points.

OBJECTIVES

:

Use the Pythagorean

Theorem to calculate

the distance between

NURWAHIDAH (091104184)

Look at the map below. It is

On the map, we can see that

distance between Tafemaar (

archipelago) and Tual (Tanimbar

archipelago) is 3 cm, and the distance

between Tual and Saumlaki (Tanimbar

Archipelago) is 4 cm. “Iramual”

motorboat sails from Tanimbar to Aru

trough Kai archipelago. While

“Isabela” motorboat sails from

Tanimbat to Aru. Which motorboat

will arrived firstly in Aru if both of the

motorboat start their sailing in the

same time and velocity?

A •USE THE PYTHAGOREAN THEOREM TO CALCULATE THE DISTANCE BETWEEN ANY TWO POINT

K

A

T Gambar 3.10


It is the map of an archipelago in Maluku.

we can see that the

distance between Tafemaar (Aru

archipelago) and Tual (Tanimbar

archipelago) is 3 cm, and the distance

between Tual and Saumlaki (Tanimbar

Archipelago) is 4 cm. “Iramual”

sails from Tanimbar to Aru

trough Kai archipelago. While

“Isabela” motorboat sails from

Tanimbat to Aru. Which motorboat

will arrived firstly in Aru if both of the

motorboat start their sailing in the

To answer the question above we must know the

distance between Aru and Tanimbar firstly. The

position of the three islands is shown on picture 7.

USE THE PYTHAGOREAN THEOREM TO CALCULATE THE DISTANCE BETWEEN ANY TWO POINT

Gambar 6

Direct Instruction

2

To answer the question above we must know the

Tanimbar firstly. The

position of the three islands is shown on picture 7.

USE THE PYTHAGOREAN THEOREM TO CALCULATE THE DISTANCE BETWEEN ANY TWO POINT

Direct Instruction


We can make a connection line among the three islands. It will be a right triangle.

So, we can make an equation:

AT2 = AK2 + KT2

= 32 + 42

= 25

AT = 25

AT = 5

Thus, the distance between Aru and Tanimbar archipelago is 5 cm in the picture.

By knowing the distance between Aru and Tanimbar, we will also know what

motorboat will arrive firstly.

Pythagorean Theorem is a simple theorem to solve many daily problem related

with plane and space geometry.

We have proved the Pythagorean Theorem in our first meeting.

to Use the Pythagorean Theorem to calculate the distance between any two points.

of the formulas below are got from Pythagorean Theorem.

Conclusion :

Remember that In a right triangle, the sum of the

squares of the lengths of the legs equals the square of

the length of the hypotenuse. If

of the legs, and c is the

a2 + b

2 = c

2



ke an equation:

the distance between Aru and Tanimbar archipelago is 5 cm in the picture.

stance between Aru and Tanimbar, we will also know what

motorboat will arrive firstly.


with plane and space geometry.

We have proved the Pythagorean Theorem in our first meeting. Therefore

Use the Pythagorean Theorem to calculate the distance between any two points.

of the formulas below are got from Pythagorean Theorem.

Remember that In a right triangle, the sum of the

squares of the lengths of the legs equals the square of

the length of the hypotenuse. If a and b are the lengths

of the legs, and c is the length of the hypotenuse, then

If �� has 90o in A, then it will fulfill:

BC2 = AC

2 + AB

2 or

a2 = b

2 + c

2

b2 = a

2 – c

2

c2 = a

2 – b

2

3


the distance between Aru and Tanimbar archipelago is 5 cm in the picture.

stance between Aru and Tanimbar, we will also know what


Therefore, we will try

Use the Pythagorean Theorem to calculate the distance between any two points. All

in A, then it will fulfill:


4 EXAMPLE A

Let �� has 90o in A. The length of AB = 4 cm and

AC = 3 cm. Determine the length of BC!

SOLUTION:

BC2 = AB2 + AC2

BC2 = 42 + 32

BC2 = 16 + 9

BC2 = 25

BC = ��

EXAMPLE B

Look at the picture. It is known that b = 6

and c = 5. Find the value of a!

a2 = b2 + c2

a2 = 62 + 52

a2 = 36 + 25

a2 = 61

a = ��

EXAMPLE C

Based on the picture, determine the value of p!

SOLUTION:

(10)2 = p2 + 62

100 = p2 + 36

100 - 36 = p2

64 = p2

p = ��

or

p2 = (10)

2 - 6

2

= 100 – 36

p2

= 64

p = ��


5 EXAMPLE D

On the picture, you can see AB= 12 cm, BC= 9 cm, and CD=25 cm. Determine the

length of AD.

SOLUTION:

��

� ��

� ��

��

��

��

��

��

��

EXAMPLE E

How high up on the wall will a 20-foot ladder

touch if the foot of the ladder is placed 5 feet

from the wall?

SOLUTION:

The ladder is the hypotenuse of a right

triangle, so

a2 + b

2 = c

2

(5)2 + (h)2 = (20)2 Subtitute

25 + h2 = 400 Multiply

h2 = 375 Substract 25 from the both sides

� � �� Take the square root of each side.

The top of the ladder will touch the wall about 19.4 feet up from the ground.

Notice that the exact answer in Example A is �� . However, this is a p ractical

application, so you need to calculate the approximate answer.


6

1. Find y on the picture below

2. The congruent sides of an isosceles triangle measure 6 cm, and the base

measures 8 cm. Find the area.

3. The diagonal of a square measures 32 meters. What is the area of the square?

4. How high on a building will a 15- foot ladder touch if the foot of the ladder is

5 feet from the building?

5. The front and back walls of an A-frame cabin

are isosceles triangles, each with a base

measuring 10 m and legs measuring 13 m. The

entire front wall is made of glass1 cm thick that

cost $120/m2.What did the glass for the front

wall cost?

Note : Number 1, 3, and 5 left as an exercise in your worksheet. Open in your worksheet, and do the exercise


7 REFERENCES

Adinawan, M.Kholik. 2003.Matematika SLTP Jilid 2A Kelas 2. Jakarta: Erlangga.

Agus,Nuniek Avianti. 2008. Mudah belajar matematika 2: untuk kelas VIII SMP/MTs. Jakarta:

Pusat Perbukuan Depdiknas.

GCSE Math Tutor. 2010. Shape and Space. United States of America: Saddleback Educational

Publishing.

Gibilisco,Stan. 2004. Everyday Math Demystified. New York : Mc Graw-Hill.

Nugroho, Heru. 2009. Matematika 2: SMP/MTs kelas VIII. Jakarta: Pusat Perbukuan

Depdiknas.

Nuhairini, Dewi. 2008.Matematika Konsep dan Aplikasi: untuk SMP/MTs kelas VIII. Jakarta:

Pusat perbukuan Depdiknas.

Rahaju, Budi Endah. 2008.Contextual Teaching and Learning Matematika: SMP/MTs kelas

VIII Edisi 4. Jakarta: Pusat perbukuan Depdiknas.

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