Download Unit 2 Review

Unit 2 Review
Short Answer
1. Find the value of x. Express your answer in
simplest radical form.
30º
x
3
6
2. The size of a TV screen is given by the length of its
diagonal. The screen aspect ratio is the ratio of its
width to its height. The screen aspect ratio of a
standard TV screen is 4:3. What are the width and
height of a 27" TV screen?
y
24
60º
x
5. Write the trigonometric ratio for cos X as a fraction
and as a decimal rounded to the nearest hundredth.
Y
15
9
height
27"
X
width
3. Find the missing side length. Tell if the side lengths
form a Pythagorean triple. Explain.
25
Z
12
6. Use your calculator to find the trigonometric ratios
sin 79 , cos 47 , and tan 77 . Round to the nearest
hundredth.
7. Use your calculator to find the trigonometric ratios
sin 49 , cos 50 , and tan 45 . Round to the nearest
hundredth.
8. Find GH. Round to the nearest hundredth.
20
G
4. Find the values of x and y. Express your answers in
simplest radical form.
F
35°
18.4 in.
H
9. Jessie is building a ramp for loading motorcycles
onto a trailer. The trailer is 2.8 feet off of the
ground. To avoid making it too difficult to push a
motorcycle up the ramp, Jessie decides to make the
angle between the ramp and the ground 15 . To the
nearest hundredth of a foot, find the length of the
ramp.
10. Find the sine and cosine of the acute angles in the
right triangle.
1
1.3 cm
0.5 cm
2
3
1.2 cm
15. Use your calculator to find the angle measures
to the
nearest tenth of a degree.
16. Find
to the nearest hundredth.
B
B
2
53
45
A
C
4
17. Classify each angle in the diagram as an angle of
elevation or an angle of depression.
A
28
3
11. Find the sine and cosine of the acute angles in the
right triangle.
B
169
119
A
120
12. Write cos 16° in terms of the sine.
13. Write sin 74° in terms of the cosine.
14. Use the trigonometric ratio
to
determine which angle of the triangle is
.
4
2
1
18. The largest Egyptian pyramid is 146.5 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.
19. An eagle 300 feet in the air spots its prey on the
ground. The angle of depression to its prey is 15 .
What is the horizontal distance between the eagle
and its prey? Round to the nearest foot.
20. A pilot flying at an altitude of 1.8 km sights the
runway directly in front of her. The angle of
depression to the beginning of the runway is 31 .
The angle of depression to the end of the runway is
23. What is the length of the runway? Round to
the nearest tenth of a kilometer.
Unit 2 Review
Answer Section
SHORT ANSWER
1. ANS:
x=
Pythagorean Theorem
Substitute 3 for a, 6 for b, and x for c.
Simplify.
Find the positive square root.
Simplify the radical.
PTS: 1
DIF: 2
REF: 1af8a14a-4683-11df-9c7d-001185f0d2ea
OBJ: 9-1.1 Using the Pythagorean Theorem
STA: MCC9-12.G.SRT.8
LOC: MTH.C.10.05.10.05.01.001 | MTH.C.11.03.02.05.02.002
TOP: 9-1 The Pythagorean Theorem
KEY: Pythagorean Theorem | side length
DOK: DOK 1
2. ANS:
width: 21.6 in., height: 16.2 in.
Let 3x be the height in inches. Then 4x is the width of the TV screen.
Pythagorean Theorem
Substitute 4x for a, 3x for b, and 27 for c.
Multiply and combine like terms.
Divide both sides by 25.
Find the positive square root.
in.
Width:
Height:
in.
in.
PTS: 1
DIF: 2
REF: 1afadc96-4683-11df-9c7d-001185f0d2ea
OBJ: 9-1.2 Application
NAT: NT.CCSS.MTH.10.9-12.G.SRT.8
STA: MCC9-12.G.SRT.8
LOC: MTH.C.10.05.10.05.01.001 | MTH.C.11.03.02.05.02.002
TOP: 9-1 The Pythagorean Theorem
KEY: Pythagorean Theorem | side length
DOK: DOK 1
3. ANS:
The missing side length is 15. The side lengths form a Pythagorean triple because they are nonzero whole numbers
that satisfy the equation
.
Pythagorean Theorem
Substitute 20 for a and 25 for c.
Multiply and subtract 400 from both sides.
Find the positive square root.
The side lengths are nonzero whole numbers that satisfy the equation
triple.
PTS:
OBJ:
LOC:
TOP:
DOK:
4. ANS:
, so they form a Pythagorean
1
DIF: 1
REF: 1afd3ef2-4683-11df-9c7d-001185f0d2ea
9-1.3 Identifying Pythagorean Triples
STA: MCC9-12.A.REI.4b
MTH.C.11.03.02.05.02.002 | MTH.C.11.03.02.05.02.004
9-1 The Pythagorean Theorem
KEY: Pythagorean Theorem | side length | Pythagorean triple
DOK 2
,
Hypotenuse
Divide both sides by 2.
PTS:
OBJ:
LOC:
TOP:
DOK:
5. ANS:
1
DIF: 2
REF: 1b046606-4683-11df-9c7d-001185f0d2ea
9-2.3 Finding Side Lengths in a 30-60-90 Triangle
STA: MCC9-12.G.SRT.6
MTH.C.11.03.02.05.03.001 | MTH.C.11.03.02.05.03.002
9-2 Applying Special Right Triangles
KEY: special right triangles | 30-60-90
DOK 2
cos X =
cos X =
The cosine of an
is
.
PTS: 1
DIF: 1
REF: 1bc0c06a-4683-11df-9c7d-001185f0d2ea
OBJ: 10-1.1 Finding Trigonometric Ratios
NAT: NT.CCSS.MTH.10.9-12.G.SRT.6
STA: MCC9-12.G.SRT.6
LOC: MTH.C.14.02.01.002 | MTH.C.14.02.02.004
TOP: 10-1 Trigonometric Ratios
KEY: trigonometric ratio | trigonometry | cosine
DOK: DOK 2
6. ANS:
sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33
Make sure your calculator is in degree mode.
sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33
PTS: 1
DIF: 1
REF: 1bc349d6-4683-11df-9c7d-001185f0d2ea
OBJ: 10-1.3 Calculating Trigonometric Ratios
NAT: NT.CCSS.MTH.10.K-12.5.1
TOP: 10-1 Trigonometric Ratios
KEY: trigonometric ratio | trigonometry | cosine | sine | tangent
DOK: DOK 2
7. ANS:
sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1
Make sure your calculator is in degree mode.
sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1
PTS: 1
DIF: 1
REF: 1bc349d6-4683-11df-9c7d-001185f0d2ea
OBJ: 10-1.3 Calculating Trigonometric Ratios
NAT: NT.CCSS.MTH.10.K-12.5.1
TOP: 10-1 Trigonometric Ratios
KEY: trigonometric ratio | trigonometry | cosine | sine | tangent
DOK: DOK 2
8. ANS:
GH = 22.46 in.
GH is the length of the hypotenuse of the triangle. You are given FH, which is adjacent to
. Since the adjacent
side and hypotenuse are involved, use the cosine ratio.
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by GH and divide by cos 35 .
in
Simplify the expression.
PTS: 1
DIF: 2
REF: 1bc58522-4683-11df-9c7d-001185f0d2ea
OBJ: 10-1.4 Using Trigonometric Ratios to Find Lengths
STA: MCC9-12.G.SRT.8
LOC: MTH.C.14.02.03.001
TOP: 10-1 Trigonometric Ratios
KEY: trigonometric ratio | trigonometry | side length
DOK: DOK 2
9. ANS:
10.82 feet
B
2.8 ft
A

C
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by AB and divide by sin 15 .
feet
PTS:
OBJ:
STA:
TOP:
DOK:
10. ANS:
1
DIF: 2
REF: 1bc7e77e-4683-11df-9c7d-001185f0d2ea
10-1.5 Problem-Solving Application
NAT: NT.CCSS.MTH.10.9-12.G.SRT.8
MCC9-12.G.SRT.8
LOC: MTH.C.14.02.03.001
10-1 Trigonometric Ratios
KEY: trigonometric ratio | trigonometry | side length
DOK 2
45
; cos A =
53
28
sin B =
; cos B =
53
sin A =
Simplify the expression.
28
53
45
53
PTS:
OBJ:
STA:
KEY:
11. ANS:
1
DIF: 1
REF: 91632d45-6ab2-11e0-9c90-001185f0d2ea
10-1-Ext.1 Finding the Sine and Cosine of Acute Angles NAT: NT.CCSS.MTH.10.9-12.G.SRT.7
MCC9-12.G.SRT.7
TOP: 10-1-Ext Trigonometric Ratios and Complementary Angles
right triangle trigonometry | sine | cosine | tangent
DOK: DOK 2
119
; cos A =
169
120
sin B =
; cos B =
169
sin A =
120
169
119
169
PTS: 1
DIF: 1
REF: 91632d45-6ab2-11e0-9c90-001185f0d2ea
OBJ: 10-1-Ext.1 Finding the Sine and Cosine of Acute Angles NAT: NT.CCSS.MTH.10.9-12.G.SRT.7
STA: MCC9-12.G.SRT.7
TOP: 10-1-Ext Trigonometric Ratios and Complementary Angles
KEY: right triangle trigonometry | sine | cosine | tangent
DOK: DOK 2
12. ANS:
sin 74°
PTS: 1
DIF: 2
REF: 91635455-6ab2-11e0-9c90-001185f0d2ea
OBJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms
NAT: NT.CCSS.MTH.10.9-12.G.SRT.7 STA: MCC9-12.G.SRT.7
TOP: 10-1-Ext Trigonometric Ratios and Complementary Angles
KEY: right triangle trigonometry | cosine | sine
DOK: DOK 1
13. ANS:
cos 16°
PTS:
OBJ:
NAT:
TOP:
KEY:
14. ANS:
2
1
DIF: 2
REF: 91635455-6ab2-11e0-9c90-001185f0d2ea
10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms
NT.CCSS.MTH.10.9-12.G.SRT.7 STA: MCC9-12.G.SRT.7
10-1-Ext Trigonometric Ratios and Complementary Angles
right triangle trigonometry | cosine | sine
DOK: DOK 1
Sine is the ratio of the opposite leg to the hypotenuse.
1.2 is the length of the leg opposite
1.3 is the length of the hypotenuse.
0.5 is the length of the leg adjacent
1.3 is the length of the hypotenuse.
Since
PTS:
OBJ:
LOC:
KEY:
15. ANS:
,
2 is
.
.
A.
1
DIF: 2
REF: 1bc80e8e-4683-11df-9c7d-001185f0d2ea
10-2.1 Identifying Angles from Trigonometric Ratios
STA: MCC9-12.G.SRT.8
MTH.C.14.02.03.002 | MTH.C.14.02.001
TOP: 10-2 Solving Right Triangles
trigonometric ratio | trigonometry DOK: DOK 2
= 44.4°,
= 72.5°,
= 88.5°
Change your calculator to degree mode.
Use the inverse trigonometric functions on your calculator to find each angle measure.
PTS:
OBJ:
NAT:
LOC:
TOP:
DOK:
16. ANS:
1
DIF: 1
REF: 1bca49da-4683-11df-9c7d-001185f0d2ea
10-2.2 Calculating Angle Measures from Trigonometric Ratios
NT.CCSS.MTH.10.9-12.F.TF.7
STA: MCC9-12.G.SRT.8
MTH.C.14.04.01.002 | MTH.C.14.04.02.002 | MTH.C.14.04.03.002
10-2 Solving Right Triangles
KEY: trigonometric ratio | trigonometry | inverse trigonometric ratio
DOK 1
= 0.45
By the Pythagorean Theorem,
.
PTS: 1
DIF: 2
REF: 1bccac36-4683-11df-9c7d-001185f0d2ea
OBJ: 10-2.3 Solving Right Triangles
STA: MCC9-12.G.SRT.8
LOC: MTH.C.14.02.02.002
TOP: 10-2 Solving Right Triangles
KEY: trigonometric ratio | trigonometry | solve right triangles
DOK: DOK 2
17. ANS:
Angles of elevation: 1, 3
Angles of depression: 2, 4
1 and 3 are formed by a horizontal line and a line of sight to a point above the line. They are angles of
elevation.
2 and 4 are formed by a horizontal line and a line of sight to a point below the line. They are angles of
depression.
PTS:
OBJ:
LOC:
KEY:
18. ANS:
402 m
1
DIF: 1
REF: 1bd170ee-4683-11df-9c7d-001185f0d2ea
10-3.1 Classifying Angles of Elevation and Depression
STA: MCC9-12.G.SRT.8
MTH.C.11.02.04.10.001 | MTH.C.11.02.04.10.002
TOP: 10-3 Angles of Elevation and Depression
angle of elevation | angle of depression | trigonometry
DOK: DOK 1
B
146.2 m
20º
A
x
Use the side opposite
the tangent ratio.
and x, and the side adjacent to
Multiply both sides by x and divide both sides by
to write
.
Simplify.
PTS: 1
DIF: 2
REF: 1bd197fe-4683-11df-9c7d-001185f0d2ea
OBJ: 10-3.2 Finding Distance by Using Angle of Elevation
NAT: NT.CCSS.MTH.10.9-12.G.SRT.8
STA: MCC9-12.G.SRT.8
LOC: MTH.C.14.02.03.001
TOP: 10-3 Angles of Elevation and Depression
KEY: angle of elevation | angle of depression | trigonometry
DOK: DOK 2
19. ANS:
1,120 ft
R
15º
300 ft
15º
S
x
By the Alternate Interior Angles Theorem, m
. From the sketch,
. So
PTS: 1
DIF: 2
REF: 1bd3d34a-4683-11df-9c7d-001185f0d2ea
OBJ: 10-3.3 Finding Distance by Using Angle of Depression
NAT: NT.CCSS.MTH.10.9-12.G.SRT.8
STA: MCC9-12.G.SRT.8
LOC: MTH.C.14.02.03.001
TOP: 10-3 Angles of Elevation and Depression
KEY: angle of elevation | angle of depression | trigonometry
DOK: DOK 2
20. ANS:
1.2 km
A
23°

1.8 km

D
23°
C
B
Step 1 Draw a sketch. Let B and C represent the beginning and end of the runway. Let CB be the length of the
runway.
Step 2 Find
.
By the Alternate Interior Angles Theorem, m
In 
,
So
Step 3 Find
.
By the Alternate Interior Angles Theorem, m
In 
,
Step 4 Find
.
.
So
.
So the runway is about 1.2 km long.
PTS: 1
DIF: 2
REF: 1bd3fa5a-4683-11df-9c7d-001185f0d2ea
.
OBJ:
STA:
TOP:
KEY:
10-3.4 Application
NAT: NT.CCSS.MTH.10.9-12.G.SRT.8
MCC9-12.G.SRT.8
LOC: MTH.C.14.02.03.001
10-3 Angles of Elevation and Depression
angle of elevation | angle of depression | trigonometry
DOK: DOK 2