Chapter 7 Vocabulary

1
Chapter 7 Vocabulary
2
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!!!!!!!!!!!

3
(No Transcript)
4
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 - - 27
9
Stated 9 is the Geometric Mean of 3 and 27.
5
Geometric Mean Theorem 1 (Page 343)
Chapter 7 Vocabulary
An altitude drawn from the vertex (right angle)
of a right triangle to its hypotenuse divides
the right triangle into 2 similar triangles.
A
D
B
C
Stated D ADB D BDC
6
Geometric Mean Theorem 2 (Page 343)
Chapter 7 Vocabulary
An altitude drawn from the vertex (right angle)
of a right triangle to its hypotenuse is the
geometric mean of the two segments of the
hypotenuse
A
D
B
C
7
Chapter 7 Vocabulary
Geometric Mean Theorem 3 (Page 344)
An altitude drawn from the vertex (right angle)
of a right triangle to its 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
8
Geometric Mean Theorem 3 (Page 344)
Chapter 7 Vocabulary
An altitude drawn from the vertex (right angle)
of a right triangle to its 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
9
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
30
45
10
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
A d j a c e n t
H y p o t e n u s e
H y p o t e n u s e
A d j a c e n t
O p p o s i t e
11
Chapter 7 Vocabulary
Sine (Page 364)
The opposite side divided by the hypotenuse.
Sine 3 (opposite) 5
(hypotenuse)
5
3
4
12
Chapter 7 Vocabulary
Cosine (Page 364)
The adjacent side divided by the hypotenuse.
Cosine 4 (adjacent) 5
(hypotenuse)
5
3
4
13
Chapter 7 Vocabulary
Tangent (Page 364)
The opposite side divided by the adjacent.
Tangent 3 (opposite) 4
(adjacent)
5
3
4
14
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.
15
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 50 86.595
Tan .5774
50 feet
30o
86.595 feet
16
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.
17
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?
50 feet
Sin 50 100
100 feet
Sin .5
30o
18
Chapter 7 Vocabulary
Law of Sines (Page 377)
SinA SinB SinC a b c
A
c
b
a
B
C
19
Chapter 7 Vocabulary
Law of Sines (DEMO) (Page 377)
What is the measure of angle B in the triangle
below?
SinA SinB SinC a b c
1 Sin B 4 4
Sin 30o Sin B 2 4
.5 Sin B 2 4
Sin C Sin B 2 4
B
4Sin B 4
Sin B 1
B 90o
a
c
b
30o
C
A
20
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
B
C
21
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
30o
C
A
c2 a2 b2 2 (a)(b)(Cosine C)
22
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
23
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
30o
C
A
b2 a2 c2 2 (a)(c)(Cosine B)
24
b2 a2 c2 2 (a)(c)(Cosine B)
b2 ( )2 (2)2 2( )(2)(Cosine
90o)
b2 12 4 (13.856)(0)
b2 12 4
b2 16
b 4
25
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
30o
C
A
a2 b2 c2 2 (b)(c)(Cosine A)
26
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
27
(No Transcript)
28
(Undefined)
Tan p/2 Sin p/2 Cos p/2
29
(No Transcript)