Download Chapter 7 - Angelfire

SCHOOL CREED
•I have faith in myself
•I have faith in my teachers
•I will accept my duties and responsibilities
•I will respect others and seek their respect
•I have self respect
•I have self control
•I can learn if I study hard
•I will learn because I will study hard
•I love myself
•And loving myself
•I'll be myself
•And know myself`
•I am the one who is talking
•Balance
•Order
•Harmony
•Reciprocity
•Truth
•Justice
•Righteousness
•Look around you
•And behold us in our greatness
•Greatness is a Panther Possibility
•And you can make it yours!!!!!!!!!!!
Chapter 7 Vocabulary
Geometric Mean: (Page 342)
The Positive square root of the product of two numbers. X = M
M Y
3 = M
M 27
M=9
M2 = 81
3 -9 - 27
Stated: “9 is the Geometric Mean of 3 and 27.”
Chapter 7 Vocabulary
Geometric Mean Theorem #1: (Page 343)
An altitude drawn from the vertex (right angle) of a right triangle
to it’s hypotenuse divides the right triangle into 2 similar triangles.
A
D
B
C
Stated: D ADB ~ D BDC
Chapter 7 Vocabulary
Geometric Mean Theorem #2: (Page 343)
An altitude drawn from the vertex (right angle) of a right triangle
to it’s hypotenuse is the geometric mean of the two segments of
the hypotenuse
A
D
B
C
Chapter 7 Vocabulary
Geometric Mean Theorem #3: (Page 344)
An altitude drawn from the vertex (right angle) of a right triangle
to it’s hypotenuse makes the measure of any leg of the triangle the
geometric mean of the the measures of the entire hypotenuse and
the segment of the hypotenuse adjacent to that leg.
A
D
B
C
Chapter 7 Vocabulary
Geometric Mean Theorem #3: (Page 344)
An altitude drawn from the vertex (right angle) of a right triangle
to it’s hypotenuse makes the measure of any leg of the triangle the
geometric mean of the the measures of the entire hypotenuse and
the segment of the hypotenuse adjacent to that leg.
A
D
B
C
Chapter 7 Vocabulary
Pythagorean Theorem: a2 + b2 = c2 (Page 350)
Pythagorean Triple (Page 352): Three numbers satisfying the equation
a2 + b2 = c2
45-45-90 SRT: The hypotenuse is radical 2 times the length of the
other two equal sides. (Page 357)
30-60-90 SRT: The hypotenuse is 2 times the length of the short
leg while the long leg is radical 3 times the length of the short leg.
(Page 359)
60
45
45
30
Trigonometry: (Page 364)
Chapter 7 Vocabulary
The study of the measurement of triangles
Trigonometric Ratios: (Page 364)
Ratios found through the division of the lengths of the sides of
a right triangle.
O
p
p
o
s
i
t
e
Hypotenuse
Adjacent
A
d
j
a
c
e
n
t
Hypotenuse
Opposite
Chapter 7 Vocabulary
Sine: (Page 364)
The opposite side divided by the hypotenuse.
Sine
5
3
4
= 3 (opposite)
5 (hypotenuse)
Chapter 7 Vocabulary
Cosine: (Page 364)
The adjacent side divided by the hypotenuse.
Cosine
5
3
4
= 4 (adjacent)
5 (hypotenuse)
Chapter 7 Vocabulary
Tangent: (Page 364)
The opposite side divided by the adjacent.
Tangent
5
3
4
= 3 (opposite)
4 (adjacent)
Chapter 7 Vocabulary
Angle of Elevation: (Page 371)
The angle between the line of sight and the horizontal (adjacent)
side when the observer looks up.
Chapter 7 Vocabulary
Angle of Elevation DEMO: (Page 371)
What is the angle of elevation required to intercept a bird
traveling the given distance at an altitude of 50 feet?
Tan
Tan
= 50
86.595
= .5774
50 feet
~ 30o
86.595 feet
Chapter 7 Vocabulary
Angle of Depression: (Page 372)
The angle between the line of sight and the horizontal (adjacent)
side when the observer looks down.
Chapter 7 Vocabulary
Angle of Depression DEMO: (Page 372)
What is the angle of decent of a bird traveling along a 100 foot
diagonal from an altitude of 50 feet?
Sin
Sin
= 50
100
= .5
= 30o
50 feet
100 feet
Chapter 7 Vocabulary
Law of Sines: (Page 377)
SinA = SinB = SinC
a
b
c
A
c
b
a
B
C
Chapter 7 Vocabulary
Law of Sines (DEMO): (Page 377)
SinA = SinB = SinC
a
b
c
What is the measure of angle B in the
triangle below?
Sin 30o = Sin B
2
4
Sin C = Sin B
2
4
.5 = Sin B
2
4
B
1 = Sin B
4
4
4Sin B = 4
Sin B = 1
a
c
b
A
B = 90o
30o
C
Chapter 7 Vocabulary
Law of Cosines: (Page 385)
a2 = b2 + c2 – 2 (b)(c)(Cosine A)
b2 = a2 + c2 – 2 (a)(c)(Cosine B)
c2 = a2 + b2 – 2 (a)(b)(Cosine C)
A
c
b
a
C
B
Chapter 7 Vocabulary
Law of Cosines (DEMO #1): (Page 385)
What is the length of side AB in the triangle below?
B
a
c
b
A
c2 = a2 + b2 – 2 (a)(b)(Cosine C)
30o
C
c2 = a2 + b2 – 2 (a)(b)(Cosine C)
c2 = (
)2 + (4)2 – 2(
)(4)(Cosine 30o)
c2 = 12 + 16 – (27.713)(.8660)
c2 = 12 + 16 – 24.00016
c2 = 12 – 8.00016
c2 = 3.9984
c = 1.999 ~ 2
Law of Cosines (DEMO #2): (Page 385)
Chapter 7 Vocabulary
What is the length of side AC in the triangle below?
B
a
c
b
A
b2 = a2 + c2 – 2 (a)(c)(Cosine B)
30o
C
b2 = a2 + c2 – 2 (a)(c)(Cosine B)
b2 = (
)2 + (2)2 – 2(
b2 = 12 + 4 – (13.856)(0)
b2 = 12 + 4
b2 = 16
b =4
)(2)(Cosine 90o)
Law of Cosines (DEMO #3): (Page 385)
Chapter 7 Vocabulary
What is the length of side BC in the triangle below?
B
a
c
b
A
a2 = b2 + c2 – 2 (b)(c)(Cosine A)
30o
C
a2 = b2 + c2 – 2 (b)(c)(Cosine A)
a2 = (4 )2 + (2)2 – 2(4)(2)(Cosine 60o)
a2 = 16 + 4 – (16)(.5)
a2 = 16 + 4 – 8
a2 = 16 – 4
a2 = 12
a=
a=
a=
(Undefined)
Tan p/2 = Sin p/2
Cos p/2