Download Unit 8 Review and Answers

Name: ________________________ Class: ___________________ Date: __________
Geometry - Chapter 8 Review 1516
Short Answer
1. Write a similarity statement comparing the three triangles in the diagram.
2. Find sin ∠A to the nearest hundredth.
3. The coordinates of the vertices of ∆RPQ are R(2,−1), P(2,2), and Q(−2,−1) . Find m∠P .
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ID: A
Name: ________________________
ID: A
4. To estimate the height of a radio tower, Jody steps 25 feet away from the center of the tower’s base, until his
line of sight to the top of the tower and his line of sight to the center of its base form a right angle. His eyes
are 6 feet above the ground. How tall is the radio tower to the nearest foot?
5. Find two angles that satisfy the equation sin(4x + 14)° = cos(–3x + 73)°.

→
6. Write the vector AB in component form.
7. The largest Egyptian pyramid is 146.2 m high. When Rowena stands far away from the pyramid, her line of
sight to the top of the pyramid forms an angle of elevation of 20° with the ground. What is the horizontal
distance between the center of the pyramid and Rowena? Round to the nearest meter.
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Name: ________________________
ID: A
Completion
Complete each statement.
8. Label the angles and side relationships for the 30-60-90 triangle by filling in the 6 boxes with the correct
values/expressions.
9. Label the angles and side relationships for the 45-45-90 triangle by filling in the 6 boxes with the correct
values/expressions.
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Name: ________________________
ID: A
Matching
Match each vocabulary term with its definition.
a. cosine
b. adjacent leg
c. sine
d. tangent
e. trigonometric ratio
f. angle of depression
g. opposite leg
h. angle of elevation
i. geometric mean
____ 10. the angle formed by a horizontal line and a line of sight to a point above
____ 11. for positive numbers a and b, the positive number x such that
a x
=
x b
____ 12. the angle formed by a horizontal line and a line of sight to a point below
____ 13. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the hypotenuse
____ 14. in a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse
____ 15. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the
angle
____ 16. a ratio of two sides of a right triangle
Match each vocabulary term with its definition.
a. parallel vectors
b. resultant vector
c. additive vector
d. direction
e. equal vectors
f. magnitude
g. multiplicative vector
h. component form
i. vector
____ 17. the form of a vector that lists the vertical and horizontal change from the initial point to the terminal point
____ 18. a quantity that has both magnitude and direction
____ 19. two vectors that have the same magnitude and the same direction
____ 20. vectors with the same or opposite direction
____ 21. the vector that represents the sum of two given vectors
| → | | → |
____ 22. the length of a vector, written | AB | or | v |
|
| | |
____ 23. the orientation of a vector, which is determined by the angle the vector makes with a horizontal line
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ID: A
Geometry - Chapter 8 Review 1516
Answer Section
SHORT ANSWER
1. ANS:
∆GFJ ∼ ∆GHF ∼ ∆FHJ
TOP: 8-1 Similarity in Right Triangles
2. ANS:
sin ∠A = 0.45
TOP: 8-3 Solving Right Triangles
3. ANS:
m∠P = 53°
TOP: 8-3 Solving Right Triangles
4. ANS:
110 feet
TOP: 8-1 Similarity in Right Triangles
5. ANS:
26°; 64°
TOP: 8-2-Ext. Trigonometric Ratios and Complementary Angles
6. ANS:
5, − 3
TOP: 8-6 Vectors
7. ANS:
402 m
TOP: 8-4 Angles of Elevation and Depression
COMPLETION
8. ANS: TBD
9. ANS: TBD
MATCHING
10.
11.
12.
13.
ANS:
ANS:
ANS:
ANS:
H
I
F
C
TOP:
TOP:
TOP:
TOP:
8-4 Angles of Elevation and Depression
8-1 Similarity in Right Triangles
8-4 Angles of Elevation and Depression
8-2 Trigonometric Ratios
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ID: A
14. ANS: A
15. ANS: D
16. ANS: E
TOP: 8-2 Trigonometric Ratios
TOP: 8-2 Trigonometric Ratios
TOP: 8-2 Trigonometric Ratios
17.
18.
19.
20.
21.
22.
23.
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
H
I
E
A
B
F
D
8-6 Vectors
8-6 Vectors
8-6 Vectors
8-6 Vectors
8-6 Vectors
8-6 Vectors
8-6 Vectors
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