section 8.4 special right triangles very very very very important sat section

Section 8.4 Section 8.4

Special Right TrianglesSpecial Right Triangles

VERY VERY VERY VERY VERY VERY VERY VERY

IMPORTANT SAT SECTIONIMPORTANT SAT SECTION

Draw the following.Draw the following.1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 45The remaining angles are 45oo..

3)3) One leg has a length of 4. One leg has a length of 4.

4)4) Find the missing lengths. Use Find the missing lengths. Use

Pythagorean Theorem and Pythagorean Theorem and

your mind!your mind!

5)5) HINT: You have two HINT: You have two

congruent angles!congruent angles!

45o

45o

4

4

4 2

Draw the following.Draw the following.

1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 45The remaining angles are 45oo..

3)3) One leg has a length of 17. One leg has a length of 17.

4)4) Find the missing lengths.Find the missing lengths.

17

17

45o

45o

17 2

Draw the Draw the following.following.

1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 45The remaining angles are 45oo..

3)3) One leg has a length of . One leg has a length of .

4)4) Find the missing lengths.Find the missing lengths.

5

45o

45o

5

5

10

What is the formula?What is the formula?

45

45

45 – 45 – 90 Triangle

a

a

2a

Practice Problem #1Practice Problem #1

y

8

x

45

45

45

45

a

a

2a

a = 8

x = 8

8 2y o

o

o

o

45

45

a

a

2a

Practice Problem #2Practice Problem #28 2a 8 2

2 2

a

x

y

o

o

45o

45o

8

WORK BACKWARDS!

8 2

2 2a

8 24 2

2a x y

Draw the following.Draw the following.1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 30The remaining angles are 30oo and 60 and 60oo..

3)3) One leg has a length of 7 (opposite of One leg has a length of 7 (opposite of

3030oo). ).

4)4) The hypotenuse is 14.The hypotenuse is 14.

5)5) Find the missing leg length.Find the missing leg length.

30o

60o

7

147 3

Draw the following.Draw the following.1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 30The remaining angles are 30oo and 60 and 60oo..

3)3) One leg has a length of 11 One leg has a length of 11 (opposite (opposite

3030oo))..

4)4) The hypotenuse is 22. The hypotenuse is 22.

5)5) Find the missing leg length.Find the missing leg length.

30o

60o

11

2211 3

Draw the following.Draw the following.

1)1) Draw a right triangle.Draw a right triangle.

2)2) The remaining angles are 30The remaining angles are 30oo and and

6060oo..

3)3) One leg has a length of Opp of One leg has a length of Opp of

3030oo. .

4)4) Find the missing length.Find the missing length.

5

30o

60o

5

2 515

30

60

o

o

What is the formula?What is the formula?

30 – 60 – 90 Triangle

a

2a3a

y

8x

30

60

Practice Problem #3Practice Problem #3

3x a

WORK BACKWARDS! 30

60o

a

2a3a

o

8 = 2a

a = 4 which is y so y = 4

4 3x

PRACTICEPRACTICE

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