OBJECTIVE

• I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.

leg - sides adjacent to right angle

leg

hypotenuse - longest side- opposite of right angle

Right angle - one 900 angle

The Right Triangle

What is the Pythagorean Theorem?• The theorem that the sum of the squares of

the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse.

• Used to find the missing side of a triangle when two sides are given

*Only works with right triangles

a2 b2 c 2The formula is:

- where a and b are the legs of a triangle and c is the hypotenuse of the triangle

1. Square both legs

3 ft

4 ft

4ft

3 ft

1 3

4 5 6

7 8 9

1

2

2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

2. Count the total squares

3 ft

4 ft

4ft

3 ft

1 3

4 5 6

7 8 9

1

2

2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

9 + 16 = 25

3 ft

4 ft

4ft

3 ft

1 3

4 5 6

7 8 9

1

2

2 3 45 6 7 8

9 10 11 1213 14 15 16

9 + 16 = 25

3. Put that number of squares on the hypotenuse

2

4

6

8

10

12

14

16

18

20

22

24

1

3

5

7

9

11

13

15

17

19

21

23

25

3 ft

4 ft

4ft

3 ft

1 3

4 5 6

7 8 9

1

2

2 3 45 6 7 8

9 10 11 1213 14 15 16

9 + 16 = 25

4. Count the number of squares that touch the hypotenuse.

2

4

6

8

10

12

14

16

18

20

22

24

1

3

5

7

9

11

13

15

17

19

21

23

25

# = 5

3 ft

4 ft

4ft

3 ft

1 3

4 5 6

7 8 9

1

2

2 3 45 6 7 8

9 10 11 1213 14 15 16

9 + 16 = 25

5.That number is the length of the hypotenuse.

2

4

6

8

10

12

14

16

18

20

22

24

1

3

5

7

9

11

13

15

17

19

21

23

25

# = 5Length = 5

Using the Pythagorean Theorem

– Start with the formula – Determine what numbers go with the

variables a, b, and c• a and b are the legs• c is the hypotenuse

– Substitute the numbers into the formula and solve

a2 b2 c 2

Example - Finding the Hypotenuse

a = 6

b = 8

c = ?

Equation

Substitute

Exponents

Add

Find Square Root

Length must be positive

a2 b2 c 2

62 82 c 2

36 64 c 2

c 2 100

c 2 100

c 10

c 10

Guided Practice

Find the length of the hypotenuse.

Finding a Leg• Find the leg of a right triangle with one leg

that is 9cm and a hypotenuse of 12cm.

Equation

Substitute

Subtract 81 from both sides

Find Square Root

Length is Positive

The other leg is 12cm.

a2 b2 c 2

92 b2 152

81 b2 225

b2 144

b2 144

c 12

c 12

Guided Practice

• Find the leg of a right triangle with one leg that is 12cm and a hypotenuse of 20cm.

Independent Practice

1. Find the hypotenuse of a right triangle with legs of 3in and 4in.

2. Find the leg of a right triangle with a leg of 15ft and a hypotenuse of 25 feet.