Download ACT Review Worksheet – Trigonometry Name

ACT Review Worksheet – Trigonometry
Name: ___________________________________
36. What is the cosine of angle A in right triangle
ABC below?
2
58. A 8-foot ladder leaning against the wall makes a
60  angle with the floor. What is the height H of the
ladder where it touches the wall?
F.
5
2
G.
3
5
H.
3
5
J.
2
3
F. 8 sin 60
G. 8 cos 60
H. 8 tan 60
J.
8
sin 60
K.
5
K.
24. For right triangle RST shown below, what is tan R ?
F.
r
s
G.
r
t
H.
t
r
J.
t
s
K.
s
t
8
cos 60
22. An object 4 feet tall casts a 3-foot shadow when the
angle of elevation of the sun is  what is tan(
3
F.
4
G. 1
H.
4
3
J. 7
K. 12
43. Based on the triangle shown below, what is cos y?
3
4
3
4
5
A.
B.
C.
D.
E.
5
5
4
3
3
45. The sides of a triangle are 5, 12 and 13 inches
long. What is the angle between the 2 shortest
sides?
A. 30 
B. 45 
C. 60 
D. 90 
E. 120 
12
5
34. If sin  13 and cos  = 13 , then tan 
F.
J.
5
12
7
13
G.
12
5
K.
17
13
H.
60
13
40.
CD is an altitude of equilateral triangle ABC. If CD
is 6 3 units long, how many units long is AC ?
F. 3 3
G. 6
H. 12
J. 12 3
K. 36
50. In the right angle triangle below, if C has a sine of,
2
a cosine of
29
5
, and a tangent of 2 , how many
5
29
inches long is AB ?
F.
50. In ABC , shown below, the measure of B is 41º,
the measure of C is 34º, and AB is 25 units long.
Which of the following is an expression for the length,
in units, of BC ? (Note: The law of sines states that,
for any triangle, the ratios of the sines of the interior
angles to the lengths of the sides opposite those angles
are equal.)
2
5
G. 6
H.
J.
12
5
12
K.
A.
B.
29
30
C.
29
D.
E.
1
If
tangent
of
an
angle
is
, what is the cosine of
57.
2
the same angle?
5
A.
2
2
1
B.
2
1
C.
5
2 5
D.
5
2
E.
3
47. From a hot air balloon, the angle between a radio
antenna straight below and the base of the library
downtown is 57  . If the distance between the
radio antenna and the library is 1.3 miles, how
many miles high is the balloon?
25 sin 105 
sin 41
25 sin 105 
sin 34
25 sin 34
sin 75
25 sin 75
sin 41
25 sin 41
sin 105
52. A surveyor took and recorded the measurements
shown in the figure below. If the surveyor wants
to use these 3 measurements to calculate the
length of the pond, which of the following would
be the most directly applicable?
F. The ratios for the side lengths of 30º-60º-90º
triangles
G. The ratios for the side lengths of 45º-45º-90º
triangles
H. The law of cosines: For any ABC , where a
is the length of the opposite A , b is the length
of the opposite B , and c is the length of the
side opposite C , a  b  c  2bc cos(A)
J. The Pythagorean theorem
K. A formula for the area of a triangle
2
FG
A. 1.3 sin 57 
B. 1.3 tan 57 
1.3
C.
sin 57
D.
1.3
cos 57 
E.
1.3
tan 57 
2
2
ANSWERS: 36H 24G 43A 34G 58F 22H
45D 40H 50H 57D 47E 50B 52H