Chapter 7 Test
____
1. How long is a string reaching from the top of a 9-ft pole to a point on the ground that is 7 ft from the base of
the pole?
a.
c.
120 ft
42 ft
b.
d.
32 ft
130 ft
____
2. A radio station is going to construct a 5-foot tower on top of a building. The tower will be supported by three
cables, each attached to the top of the tower and to points on the roof of the building that are 12 feet from the
base of the tower. Find the total length of the three cables.
a. 13 ft
c. 52 ft
b. 39 ft
d. 65 ft
____
3. Which set of lengths cannot form a right triangle?
a. 6 mm, 8 mm, 10 mm
c. 3 mm, 4 mm, 5 mm
b. 1.5 mm, 2 mm, 2.5 mm
d. 4 mm, 4 mm, 5 mm
____
4. A ship in calm seas steamed 12 km in one direction, turned and steamed 12 km in another direction, and then
returned 8 km back to its original position. The captain then plotted the ship's course on a nautical chart. She
asked her first officer to look at the chart and describe the ship's path. Did the first officer describe it as an
acute, obtuse, or right triangle? Then the second officer said she could further identify whether the path was
scalene, isosceles, or equilateral. What did she determine?
a. obtuse; scalene
c. acute; scalene
b. acute; equilateral
d. acute; isosceles
____
5. Li went for a mountain-bike ride in a relatively flat, wooded area. She rode for 4 km in one direction, then
turned and peddled 7 km in another. Finally she turned and rode 5 km in yet another direction. Stopping, Li
took out a map and drew her path. Could Li be back at her starting point? Could her path be a right triangle?
a. Yes; Yes
c. No; No
b. Yes; No
d. No; Yes
____
6. Choose the set that is the possible side lengths of a right triangle.
a. 1, 1, 2
c. 3, 4, 7
b. 1, 3 , 2
d. 3, 5, 9
7. For each set of numbers, determine whether the numbers represent the lengths of the sides of an acute
triangle, a right triangle, an obtuse triangle, or no triangle.
a. 50 , 28 , 22
b. 8, 10, 17
c. 2.8, 9.6, 20
8. Solve for a and b.
9. Find a, b, and h.
10. Given: ΔACD is a right triangle; DB is an altitude of ΔACD; BE is an altitude of ΔADB
Prove: ΔABE ∼ ΔDCB
____ 11. The shorter leg of a 30°-60°-90° triangle is 8.6 feet long. Find the perimeter.
a. ÁÊÁ 25.8 + 8.6 3 ˜ˆ˜ ft
c. ÁÊÁ 17.2 + 8.6 2 ˜ˆ˜ ft
Ë
¯
Ë
¯
b. ÊÁÁ 17.2 + 8.6 3 ˜ˆ˜ ft
Ë
¯
d. ÊÁÁ 25.8 + 8.6 2 ˜ˆ˜ ft
Ë
¯
12. Find the value of x and y.
13. What is the length of the diagonal of a square with side lengths 7 2 ?
14. Find the value of x and y.
15. Find tan B for the right triangle below:
Use a special right triangle to find the tangent of the given angle.
16. 60°
____ 17. Write cos B.
a.
15
8
b.
8
17
c.
8
15
d.
15
17
d.
3
5
____ 18. Use the diagram to find sin x as a fraction in simplest form.
a.
b.
5
12
5
13
12
13
d. 2 2
5
c.
____ 19. Find tan B for the right triangle below:
a.
4
5
b.
20. Find sin P, cos P, tan P.
4
3
c.
3
4
1.
c = _____
0.8
5
2. b = _____
3. c = _____
50
b
30°
b
b
c
1.7
1
45°
4. b = _____
14
5. a = _____
b
b
45°
6. b = _____
c
18
7. a = _____
39
8
65
c
2
60°
4
8. b = _____
9. c = _____
7 2
16
10. c = _____
11. c = _____
c
48
15
c
12
45°
c
c
9 3
60°
20
12. c = ____
13. b = _____
14. b = _____
15. b = _____
16. b = ____
16
30°
22
b
34
b
45°
125
b
b
18
35
There is a slide in the park that is 18 feet long. The ladder to the top of the slide is 7.5 feet long. If the ladder and the slide
are perpendicular, what is d, the distance from the top of the slide to the ground?
Chapter 7 Test
Answer Section
1. ANS: D
PTS: 1
DIF: Level B
REF: MGEO0018
TOP: Lesson 7.1 Apply the Pythagorean Theorem
KEY: solve | word | right triangles | Pythagorean Theorem
BLM: Application
NOT: 978-0-618-65613-4
2. ANS: B
PTS: 1
DIF: Level B
REF: MGEO0019
NAT: NCTM 9-12.PRS.2
STA: AK.AKGLE.MTH.05.10.PS-5
TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY:
word | Pythagorean Theorem
BLM: Application NOT: 978-0-618-65613-4
3. ANS: D
PTS: 1
DIF: Level B
REF: DITT0026
NAT: NCTM 9-12.GEO.1.a
TOP: Lesson 7.2 Use the Converse of the Pythagorean Theorem
KEY: right triangles | Pythagorean Theorem converse
BLM: Knowledge
NOT: 978-0-618-65613-4
4. ANS: D
PTS: 1
DIF: Level B
REF: BMGM0291
NAT: NCTM 9-12.GEO.1.a
TOP: Lesson 7.2 Use the Converse of the Pythagorean Theorem
KEY: word | classifying triangles
BLM: Knowledge NOT: 978-0-618-65613-4
5. ANS: B
PTS: 1
DIF: Level B
REF: MGEO0020
NAT: NCTM 9-12.GEO.1.a | NCTM 9-12.PRS.2 STA:
AK.AKGLE.MTH.05.10.PS-5
TOP: Lesson 7.2 Use the Converse of the Pythagorean Theorem
KEY: word | classifying triangles | right triangles
BLM: Comprehension
NOT: 978-0-618-65613-4
6. ANS: B
PTS: 1
DIF: Level B
REF: MLGE0156
TOP: Lesson 7.2 Use the Converse of the Pythagorean Theorem
KEY: right triangles | Pythagorean Theorem converse
BLM: Knowledge
NOT: 978-0-618-65613-4
7. ANS:
a. right triangle,
b. obtuse triangle,
c. no triangle
PTS: 1
DIF: Level B
REF: MLGE0159 NAT: NCTM 9-12.GEO.1.a
TOP: Lesson 7.2 Use the Converse of the Pythagorean Theorem
KEY: classifying triangles
BLM: Knowledge NOT: 978-0-618-65613-4
8. ANS:
a = 63; b = 105
PTS: 1
DIF: Level B
REF: MLGE0424 NAT: NCTM 9-12.GEO.1.d
STA: AK.AKGLE.MTH.05.10.MEA-2
TOP: Lesson 7.3 Use Similar Right Triangles
KEY: similar right triangles | geometric mean
BLM: Knowledge
NOT: 978-0-618-65613-4
9. ANS:
a = 10, b = 10 3 , h = 5 3
PTS: 1
DIF: Level B
REF: SXAM0042
TOP: Lesson 7.3 Use Similar Right Triangles
NAT: NCTM 9-12.GEO.1.b
KEY: similar right triangles | geometric mean
NOT: 978-0-618-65613-4
10. ANS:
Statements
Reasons
ΔACD is a right triangle
Given.
DB is an altitude of ΔACD
Given.
BLM: Knowledge
If the altitude is drawn to the hypotenuse of
ΔADB ∼ ΔDCB
a right triangle, then the two triangles formed
are similiar to each other.
BE is an altitude of ΔADB
Given.
If the altitude is drawn to the hypotenuse of
ΔABE ∼ ΔADB
a right triangle, then the two triangles formed
are similiar to the original triangle.
ΔABE ∼ ΔDCB
Transitive Property
PTS:
NAT:
STA:
KEY:
NOT:
11. ANS:
TOP:
KEY:
NOT:
12. ANS:
x = 15
1
DIF: Level B
REF: GE0.07.03.PF.04
NCTM 9-12.REA.4 | NCTM 9-12.GEO.1.c | NCTM 9-12.REA.3
AK.AKGLE.MTH.05.10.PS-4
TOP: Lesson 7.3 Use Similar Right Triangles
proof | similar right triangles | geometric mean
BLM: Evaluation
978-0-618-65613-4
A
PTS: 1
DIF: Level B
REF: DBXM1015
Lesson 7.4 Special Right Triangles
special right triangles | 30-60-90 triangle
BLM: Comprehension
978-0-618-65613-4
PTS:
TOP:
KEY:
BLM:
13. ANS:
14
1
DIF: Level A
REF: AGEO0706 NAT: NCTM 9-12.GEO.1.a
Lesson 7.4 Special Right Triangles
special right triangles | 45-45-90 triangle | 30-60-90 triangle
Knowledge NOT: 978-0-618-65613-4
2 , y = 15 + 15 3 or 15(1 +
3)
PTS: 1
DIF: Level B
REF: MLGE0161
KEY: special right triangles | 45-45-90 triangle
NOT: 978-0-618-65613-4
14. ANS:
x = 15, y = 15 3
TOP: Lesson 7.4 Special Right Triangles
BLM: Comprehension
PTS: 1
DIF: Level A
REF: GGEO0804
KEY: special right triangles | 30-60-90 triangle
NOT: 978-0-618-65613-4
15. ANS:
TOP: Lesson 7.4 Special Right Triangles
BLM: Knowledge
12
5
PTS: 1
DIF: Level A
STA: AK.AKGLE.MTH.05.10.MEA-2
KEY: tangent ratio
16. ANS:
3
17.
18.
19.
20.
PTS:
TOP:
KEY:
NOT:
ANS:
STA:
KEY:
NOT:
ANS:
STA:
KEY:
NOT:
ANS:
STA:
KEY:
BLM:
ANS:
REF: MLGM0046
TOP: Lesson 7.5 Apply the Tangent Ratio
BLM: Knowledge NOT: 978-0-618-65613-4
1
DIF: Level B
REF: 7f4ba77b-cdbb-11db-b502-0011258082f7
Lesson 7.5 Apply the Tangent Ratio
special right triangle | tangent ratio
BLM: Knowledge
978-0-618-65613-4
B
PTS: 1
DIF: Level A
REF: MHGM0136
AK.AKGLE.MTH.05.10.MEA-2
TOP: Lesson 7.6 Apply the Sine and Cosine Ratios
sine and cosine ratios | trigonometric ratios BLM:
Knowledge
978-0-618-65613-4
B
PTS: 1
DIF: Level B
REF: PMG80821
AK.AKGLE.MTH.05.10.MEA-2
TOP: Lesson 7.6 Apply the Sine and Cosine Ratios
trigonometric ratios | sine and cosine ratios BLM:
Knowledge
978-0-618-65613-4
B
PTS: 1
DIF: Level B
REF: XEA21403
AK.AKGLE.MTH.05.10.MEA-2
TOP: Lesson 7.6 Apply the Sine and Cosine Ratios
trigonometric ratios | sine and cosine ratios | tangent ratio
Knowledge NOT: 978-0-618-65613-4
sin P = 9 , cos P = 40 , tan P = 9
41
41
40
PTS:
TOP:
KEY:
BLM:
1
DIF: Level B
REF: GGEO0805 STA: AK.AKGLE.MTH.05.10.MEA-2
Lesson 7.6 Apply the Sine and Cosine Ratios
sine and cosine ratios | tangent ratio | trigonometric ratios
Knowledge NOT: 978-0-618-65613-4