Download Lesson 7-1: Arithmetic and Geometric Means Arithmetic Mean (AM

Chapter 7 Quiz 1 Review Material
Lesson 7-1: Arithmetic and Geometric Means
Arithmetic Mean (AM) or average: (a + b) / 2
Geometric Mean (GM): √ab
a
b
Altitude = GM of divided hypotenuse alt = √ab
Lesson 7-2: Pythagorean Theorem and Triangles
Pythagorean Theorem: a2 + b2 = c2
Remember c is the hypotenuse
Review from chapter 5: Three
numbers make a triangle if the smaller
two numbers added together is bigger
than the largest
c
a
b
Pythagorean Triples:
1) Three numbers that solve the Pythagorean theorem
2) All whole numbers (integers – no fractions or decimals)
Lesson 7-3: Special Right Triangles (45-45-90 and 30-60-90)
Side opposite 30° angle is ½ the hypotenuse
Side opposite 45° angle is ½ the hypotenuse times √2
Side opposite 60° angle is ½ the hypotenuse times √3
30-60-90
45-45-90
Right Isosceles triangle
½x √2
45°
x
45°
½x √2
45°
x√2
45°
x
x
60°
½x
x
30°
½x√3
Lesson 7-4: Trigonometry
Sine of an angle is equal to the opposite side divided by the hypotenuse
Cosine of an angle is equal to the adjacent side divided by the hypotenuse
Tangent of an angle is equal to the opposite side divided by the adjacent
A
sin A = y/z
sin B = x/z
z
x
cos A = x/z
cos B = y/z
tan A = y/x
tan B = x/y
B
C
y
7.1 Example Problems
1. 2, 18
2. 10, 24
Find x and y
Arithmetic Mean
Geometric Mean
8
6
10
6
7.2 Example Problems
Triangle
1. 2, 12, 18
Y/N
2. .3, .4, .5
Y/N
3. 5, 12, 13
Y/N
Find x, y, z
Right Triangle
Y/N
Y/N
Y/N
Pyth-Triple
Y/N
Y/N
Y/N
x
2x
9
z
16
x
y
12
7.3 Example Problems Find x, y, z
45°
8√2
60°
12
y
z
30°
45°
x
y
7.4 Example Problems Find sin A, cos A, tan A, sin B, cos B, tan B
B
13
5
A
12
C