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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
Page 301Page 301
Classroom ExercisesClassroom Exercises
#1 – 9#1 – 9
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