Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Aim: Whats so special about a 30 0...
-
Upload
nathaniel-griffin -
Category
Documents
-
view
216 -
download
0
Transcript of Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig. Aim: Whats so special about a 30 0...
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Aim: What’s so special about a 300-600-900 triangle?
Do Now:
Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC.
What is mA? mB? mACB?
What is mACD? mBCD?
A B
C
2x 2x
2xD
600600600
600 600
300 300
300 300
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
300-600-900 triangle
Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC
What is length of CD in terms of x?
A B
C
2x 2x
2x
?Pythagorean Theorem - a2 + b2 = c2
x2 + (CD)2 = (2x)2
(CD)2 = 3x2
x x
x2 + (CD)2 = 4x2
D
600
300
CD 3x
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
300-600-900 triangle
Triangle ABC is equilateral with each side equal to 6 (instead of 2x). CD is an altitude of ABC
What is length of CD?
A B
C
6 6?
Pythagorean Theorem - a2 + b2 = c2
32 + (CD)2 = (6)2
(CD)2 = 27
3 3
9 + (CD)2 = 36D
600
300
CD 3 3
3 3
CD 27
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
300-600-900 triangle
A
C
2x
xD
3x
A
6
3
33
C
D
Review the results of the first two problems.
Can you make any general conclusions?
Problem 1
Problem 2
600
300
600
300
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
300-600-900 triangle
o o oIn a 30 -60 -90 triangle:
the length of the hypotenuse is twice the
length of the shorter leg.
the length of the longer leg is 3 times
the length of the shorter leg
The side opposite the 30 angle
is 1/2 the
length of the hypotenuse
o o oIn a 30 -60 -90 triangle:
the length of the hypotenuse is twice the
length of the shorter leg.
the length of the longer leg is 3 times
the length of the shorter leg
The side opposite the 30 angle
is 1/2 the
length of the hypotenuse
600
300
s
2s3s
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
45o - 45o - 90o triangle
Do Now:Triangle ABC is an isosceles right triangle with BC =
A. What is mB?
mC?
AB?
AC?
2 2
A B
C
2 2450
450
Pythagorean Theorem - a2 + b2 = c2
x
x
x2 + x2 = ( )22 2
2x2 = ( )22 22x2 = 8
2
2
= 2x
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
45o - 45o - 90o triangle
Do Now:Triangle ABC is an isosceles right triangle with BC =
A. What AB?
AC?
A B
C
Pythagorean Theorem - a2 + b2 = c2
x
x
x2 + x2 = ( )2
2x2 = 72
x2 = 36 x = 6
26
2
6
26
6
6
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
300-600-900 triangle
Review the results of the first two problems.
Can you make any general conclusions?
Problem 1
Problem 2
A B
C
2 2
2
2
A B
C
6
66 2
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
450- 450 - 900 triangle
s
In a 450-450-900 triangle, the length of the hypotenuse is times the length of a leg.
In a 450-450-900 triangle, the length of the hypotenuse is times the length of a leg.
450
450
s
Ratio of Hypotenuse : Leg of I.R.T is always
2s
2 : 1
2
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Isosceles Right Triangle
450 – 450 - 900 triangle
B
F
E
I
H
D
G
CA
BFAB
= 1.4142 . . = 2
CGAC
= 1.4142 . . = 2
DHAD
= 1.4142 . . = 2
EIAE
= 1.4142 . . = 2
450
450
Ratio of Hypotenuse : Leg of I.R.T is always 2 : 1
cos45 2
sin45 2
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Summary of Special Angles in Trig
0 30 45 60 90
1 2 3sin 0 1
2 2 2
3 2 1cos 1 0
2 2 2
3tan 0 1 3
3UND
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Model Problem
Do Now:Triangle ABC is a 30-60-90 triangle with BC = 7
A. What is length of
AB?
AC?A B
C
7
600
300
Hypotenuse is 2 times the shorter leg
CB = 2(AB)
7 = 2(AB)
Longer leg is times the shorter leg3 3
AC = (AB) 3
AC 6.06
AC = (3.5)
3
3.5 = AB
3.5
3.5
3 3.5
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Model Problem
Do Now:Triangle ABC is an isosceles right triangle with BC = 8
A. What AB?
AC?
A B
C
x
x8
Pythagorean Theorem - a2 + b2 = c2
x2 + x2 = (8)2
2x2 = 64
x2 = 32 x = 32
24 x =
Inste
ad of
4 2
4 2
Ratio of Hypotenuse : Leg of I.R.T is always 2 : 1
2 8
8
2
x
x
2
2
8 2
2x 4 2
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Regents Prep
What is the exact sum of o 0sin60 cos90 ?
3
2+ 0
3
2
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel?
Model Problem
6 in.
600600
6 in. 6 in.
Draw an altitude of the rhombus. Label x and h as shown x
h
6 = 2xHypotenuse is 2 times the shorter leg
3 = x
h = 3 3
Longer leg is times the shorter leg3 3
A = bh = 6( ) = 31.2 in23 3
A = bh
Aim: Properties of Special Rt. Triangles Course: Alg. 2 & Trig.
Model Problem
A baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does the second baseman throw a ball to home plate?
90’
90’
Isosceles Right Triangle
90 = 127.27922’2
hypotenuse is times the length of a leg.2