Name ______Period ______Date ______

Honors Geometry Chapter 8 packet Right Triangles & Trigonometry Sections 1, 2, 3, 4 and 5

Wuthrich

Notes chapter 8 - attached *Notice website/utube inserts; find time to watch these.

Chapter 6 assignments from the textbook:

Due date / Date turned in / Assignment * Give answers in simplified radical form & round to nearest tenth / Grade
Section 1 Geometric Mean: pg. 541 – 545 # 8-11, 16 – 18, 21, 24, 32, 49, 54-57
Section 2 The Pythagorean Theorem and Its Converse: pg. 552- 555 # 8, 10, 14, 15, 16, 18, 21-23, 25, 28, 30, 41, 53-56
Use the distance formula for # 30
Section 3 Special Right Triangles: pg. 562- 566 # 8, 10, 11, 15, 16, 18-20, 24, 28, 31, 35, 40, 49, 51-53
Section 4 Trigonometry: pg. 573 – 578
# 16, 19, 22-30, 34, 36- 38, 54, 66-68
Section 5 Angles of Elevation & Depression: pg. 583- 587
# 4, 5, 9, 10, 16, 17, 28-31
Study Guide & Review: pg. 610-614
# 1, 3, 4, 10, 11-36
Practice TEST: pg. 615
# 1-13, 16, 19-22
Preparing for Assessment: pg. 618-619
# 1-5, 7-9, 11-13
Attached Review

Pre-AP Geometry Chapter 8 Notes Right Triangles & Trigonometry

Vocabulary / Definition / Illustration
Section 8.1 pg. 537
Geometric Mean

Key Concept Geometric Mean
Words
Example
THEOREM 8.1
. p
Example
THEOREMS Right Triangle Geometric Mean Theorems
Pg. 539 8.2 Geometric Mean (Altitude) Theorem
Example

Pg. 539 8.3 Geometric Mean (Leg) Theorem
Example
THEOREM 8.4 Pythagorean Theorem
Section 8.2 pg. 547
Words

Symbols

Vocabulary / Definition / Illustration
Pythagorean Triples /
Key Concept Common Pythagorean Triples
THEOREM 8.5 Converse of the Pythagorean Theorem
Words
Symbols

THEOREMS Pythagorean Inequality Theorems
8.6
Symbols

8.7
Symbols
THEOREM 8.8 45° - 45° - 90° Triangle Theorem
Section 8.3 pg. 558

THEOREM 8.9 30° - 60° - 90° Triangle Theorem
Vocabulary / Definition / Illustration
Section 8.4 pg. 568
Trigonometry
Trigonometric Ratio /
Key Concept Trigonometric Ratios
Words / Symbols
A


b

C a B
Key Concept Inverse Trigonometric Ratios
Words
Symbols
Words
Symbols
Words
Symbols
Vocabulary / Definition / Illustration
Section 8.5 pg. 580
Angle of Elevation
Angle of Depression / /



Pre-AP Geometry Chapter 8 Test Review Sections 1-5 Name ______

8-1 Geometric Mean
  • The geometric mean between two numbers is the positive square root of their product.
  • In right ∆ABC, the altitude to the hypotenuse is the geometric mean between the two segments of the hypotenuse and each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to that leg.
1. Find the geometric mean between:
a)3 and 24
b) and
c) and
2. The geometric mean between a and b is Find b if a = 2.
3. Find x, y, and z to the nearest tenth:

a)

b)

8-2 Pythagorean Theorem and Its Converse
1. Find the value of x:
a.

16

x

b.
2. Determine whether each set of measures is the sides of a right, acute or obtuse triangle.
a.
b.
3. Determine whether ∆GHI is a right triangle for the given vertices. Explain your reasoning.
a. G(2, 7), H(3, 6), I(-4, -1)
b. G(-6, 2), H(1, 12), I(-2, 1)
4. Find the value of x so that 65, 25 and x form a Pythagorean triple.
8-3 Special Right Triangles 45o – 45o – 90o 30o – 60o – 90o
x, x, x x, x , 2x
A 45-45-90 right triangle is half of a square; a 30-60-90 right triangle is half of an equilateral triangle.
1. The perimeter of a square is 30 inches. Find the length of the sides of the square and the length of the diagonal.
2. The hypotenuse of an isosceles right triangle is 35 mm. Find the length of the sides.
3. The perimeter of an equilateral triangle is 60 meters. Find the length of an altitude of the triangle.
4. An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle.
5. ∆GEC is a 30-60-90 triangle with right angle at E and is the longer leg. Find the coordinates of G in quadrant 1 for
E(1, 1) and C(4, 1).
8-4 Trigonometry

1. Solve the following right triangles:
a.

b.

c.
2. Find the sine, cosine and tangent of a 45o angle. Leave your answers in fraction form.
3. Find the sine, cosine and tangent of a 30o angle and a 60o angle. Leave your answers in fraction form.
8-5 Angles of Elevation and Depression
1. A ladder leaning against a building makes an angle of 78o with the ground. The foot of the ladder is 5 feet from the
building. How long is the ladder?
2. Find the angle of elevation of the sun when a 12.5-meter-tall telephone pole casts an 18-meter-long shadow.
3. A ski run is 1,000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.
4. A man is standing on a 40-foot ocean bluff. He can see his two dogs on the beach below. His line of sight is 6 feet
above the ground and the angles of depression to his dogs are 34o and 48o. How far apart are the dogs from each
other?