Practice Semester Exam: 2014-2015
Unit 6 Questions
6.1-1) Use the diagram.
C
b
a
h
x
y
A
B
D
c
Which is equal to h?
(A)
ay
(B)
bx
(C)
xy
(D)
ab
6.1-2) In the diagram, ABC is a right triangle with right angle C, and CD is an altitude of ABC .
C
b
a
d
A
e
D
B
c
Use the fact that ABC ACD CBD to prove a2  b2  c2 .
6.4-1) In GHI , the sine of angle G equals
2. What is the sine of angle G' ?
1
(A)
4
1
(B)
2
3
2
(C)
(D)
1
1
. GH I  is a dilation of GHI about G with a scale factor of
2
6.5-1) Let cos A  m . What is the value of sin A ?
m
(A)
(B)
1–m
(C)
(D)
1  m2
1 m
6.5-2) Use the diagram.
B
5
13
C
12
Which statement is true?
13
sin A 
(A)
5
12
cos A 
(B)
13
12
tan A 
(C)
5
A
6.5-3) In the diagram, BC < BD and BD = AD.
C
A
B
D
Which statement is true?
cos ABC  sin DAB
(A)
cos ABC  sin DAB
(B)
cos ABC  sin DAB
(C)
1  3 
6.6-1) What is cos 
 ?
 2 
(A)
30°
(B)
45°
(C)
60°
(D)
90°
6.6-2) What is tan 60°?
2
(A)
2
3
(B)
2
1
(C)
3
3
(D)
6.6-3) What is tan 1 1 ?
(A)
30°
(B)
45°
(C)
60°
(D)
90°
For question 6.7-1, use the statement below.
Given: An angle measures k°, where k > 0.
6.7-1) sin k   cos  90  k  
(A)
(B)
True
False
6.7-2) In ABC where C is a right angle, sin A 
(A)
(B)
(C)
(D)
7
4
7
3
3
4
3
7
For questions 3-4, let cos x  m .
6.7-3) cos  90  x   = m
(A)
True
(B)
False
6.7-4) sin  90  x   = m
(A)
True
(B)
False
6.7-5) Let a  cos28 . Which statement is true?
a  cos 62
(A)
a  cos 152
(B)
a  sin 62
(C)
a  sin 152
(D)
7
. What is cos B?
4
6.8-1) Use the diagram.
B
41
A
35°
x
Which is the value of x?
x  41cos35
(A)
tan 35
x
(B)
41
41
x
(C)
cos 35
41
x
(D)
tan 35
C
6.8-2) Use the diagram.
d
45°
What is the value of d ?
(A)
5
(B)
5 2
(C)
10
(D)
10 2
6.10-1) Fred stands at corner A of a rectangular field shown below. He needs to get to corner C.
A
B
9m
D
C
12 m
What is the shortest distance from A to C?
(A)
9m
(B)
13 m
(C)
15 m
(D)
21 m
6.10-2) Use the right triangle. What is the value of x?
15
x
8
What is the value of x?
7
(A)
161
(B)
(C)
7
(D)
17
6.10-3) The diagram shows a model of a closet floor on which Kim is laying carpet. (Measurements are
approximate.)
1 3
2 3
145°
145°
3 6
2 9
(a)
(b)
2
What is the area of the closet?
The carpet Kim is using is cut by the carpet store in rectangular pieces from a 4-foot wide roll.
What is the shortest length of carpet Kim would need to cover the closet floor in a single piece?
Justify your answer.
6.15H-1) (HONORS) Consider a triangle ABC. Which statement is true?
(A)
c2  a2  b2  2ab cos C
(B)
c2  a2  b2  2ab cos C
(C)
c2  a2  b2  2ab cos C
(D)
c2  a2  b2  2ab cos C
6.15H-2) (HONORS) Use the diagram.
A
7
4
B
What is cos A ?
16
(A)
56
56
(B)
16
16

(C)
56
56

(D)
16
C
9
6.16H-1) (HONORS) The diagram shows a surveyor’s map.
A
B
950 m 20°
50°
880 m
C
The surveyor is trying to measure the direct distance between points A and B, which are on opposite sides
of a lake. From point C, point A is 950 meters away in a direction 20° west of north. From point C, point
B is 880 meters away in a direction 50° east of north.
Which represents the distance between A and B?
(A)
(B)
(C)
9502  8802  2  950  880  cos70
880
950

sin 50 sin 20
950 sin 70
sin 55
6.16H-2) (HONORS) A small airplane flies due north at 150 kilometers per hour. A wind is blowing towards
the direction 60° east of north at 50 kilometers per hour. Which figure represents the final speed and
direction of the airplane?
N
N
N
N
(A) 
(B) 
(C) 
(D) 




















For questions 3-5, consider a triangle ABC and each given set of measurements.
6.16H-3) (HONORS) AB, AC, and mA are sufficient to solve the triangle using the Law of Sines.
(A)
True
(B)
False
6.16H-4) (HONORS) AB, AC, and mB are sufficient to solve the triangle using the Law of Sines.
(A)
True
(B)
False
6.16H-5) (HONORS) AB, AC, and BC are sufficient to solve the triangle using the Law of Sines.
(A)
True
(B)
False
6.16H-6) (HONORS) Given: cos 26  0.90 and sin 26  0.44
What is the approximate value of cos 154 ?
(A)
–0.90
(B)
–0.44
(C)
0.44
(D)
0.90
For questions 7-8 use the statement below.
Given: An angle measures k°, where k > 0.
6.16H-7) (HONORS) sin k   sin 180  k  
(A)
(B)
True
False
6.16H-8) (HONORS) cos k   cos 180  k  
(A)
True
(B)
False
For question 9, let cos x  m .
6.16H-9) (HONORS) cos 180  x   = m
(A)
True
(B)
False
6.16H-10) (HONORS) In triangle ABC, mB  25 , a = 6.2, and b = 4. Find all possible measures of the
remaining two angles and the third side.
6.16H-11) (HONORS) In triangle ABC, mB  25 , a = 6.2, and c = 4.
(a) Find all possible measures of the remaining two angles and the third side.
(b) Find all possible areas of the triangle
6.18H-1) (HONORS) The diagram shows a parallelogram ABCD.
B
C
5
60°
A
D
3
What is the parallelogram’s area?
7.5 3
(A)
15
(B)
15 3
(C)
30 3
(D)
6.18H-2) (HONORS) In the diagram, ABC is a non-right triangle.
C
a
b
B
c
Which describes the area of the triangle?
1
ab
(A)
2
ab sin C
(B)
1
ab sin C
(C)
2
1
ab cos C
(D)
2
A
8.7-1) Construct an equilateral triangle inscribed in circle O.
O