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Geometry B
Unit 6 Practice Test ANSWERS
Name
Date
Block
Directions: This test is written to cover Unit 6. Please answer each question to the best
of your ability. If multiple steps are required, it is expected that you will show those
steps. If the appropriate work is not shown, then points may be deducted.
1. Fill in the following trigonometric ratio, using the triangle at the right.
Leave your answers as fractions. (3 pts)
a. sin R 
3
5
b. cosT 
3
5
c. tan T 
4
3
2. Use your calculator to find the following. Round to four decimal places, if
necessary. (3 pts)
a. sin 42
0.6691
b. cos89
c. tan55
0.0175
1.4281
3. Use a calculator to find each angle measure to the nearest tenth of a degree. (3
pts)
a. sin 1 (0.28) 16.3°
 5 
b. cos1   65.4°
 12 
c. tan 1 (3.43) 73.7°
4. To the nearest tenth of an inch, what is the length of EF,
the longest side of the sail shown to the right? (2 pts)
28
EF
28
EF 
sin 65
sin 65 
EF  30.9 inches
5. Solve the triangles. Show work for credit. Round side lengths the same as the
given side and round all angles to the nearest tenth. (12 pts)
a.
XW = 18.3
312  XW 2  362
XW 2  362  312  335
XW  18.3
mY = 30.6°
mX = 59.4°
31
36
 31 
X  sin 1 

 36 
31
36
 31 
Y  cos1 

 36 
X  59.4
X  30.6
sin X 
cosY 
b.
mS = 24°
ST = 50.5
SU = 55.3
mT  66  90  180
mT  24
ST
22.5
ST  22.5  tan 66
tan 66 
ST  50.5
22.5
SU
22.5
SU 
cos66
SU  55.3
cos66 
6. A road sign says that the road ahead has a 7% grade. To the nearest hundredth
of a degree, find the angle the road makes with the horizontal. (2 pts)
7
100
1
A  tan  0.07 
tan A 
A  4.00
7. Ben is on the diving board at the pool. Jenna is in the pool, and a lifeguard sits at
her station on the opposite end of the pool. Classify each angle as an angle of
elevation or angle of depression. (2 pts)
1
depression
2
elevation
3
depression
4
elevation
8. A ranger in a lookout spots a fire in the distance. The angle of depression to the
fire is 4°, and the lookout tower is 32 meters tall. What is the horizontal distance
to the fire? Round to the nearest meter. (3 pts)
32
tan 4 
x
32
x
tan 4
x  458 meters
4°
32
4°
x
9. When the angle of elevation to the sun is 82°, a monument casts a shadow that is
5.1 feet long. What is the height of the monument? Round to the nearest tenth
of a foot. (3 pts)
h
5.1
h  5.1  tan 82
tan 82 
h
h  36.3 feet
82°
5.1
10.Use the Law of Sines or Law of Cosines to find the missing side or angle. Show
work for credit. Round all answers to the nearest tenth. (8 pts)
a. Find mR .
85.4°
b. Find HG. 61.1
sin 43 sin R

16.9
24.7
16.9sin R  24.7sin 43
sin 35 sin116

39
HG
HG sin 35  39sin116
24.7sin 43
 .9967...
16.9
R  sin 1 (.9967...)  85.4
HG 
sin R 
c. Find FE.
10.0
FE 2  5.82  6.32  2(5.8)(6.3)cos112
FE 2  100.706...
FE  10.0
39sin116
sin 35
HG  61.1
d. Find mS .
39.7°
6.22  8.82  9.42  2(8.8)(9.4)cos S
127.36  165.44cos S
127.36
 cos S
165.44
 127.36 
S  cos1 
  39.7
 165.44 
11.Find the exact (radical) values of x and y for the following.*
x =8 2
7 2
2
7 2
y=
2
x=
y=8
a.
b.
x =6
x =12
y= 2 3
y= 6 3
c.
d.
12.Find the following values.*
sin30 =
(8 pts)
1
2
(3 pts)
tan30 =
sin 45 =
2
2
tan 45 = 1
sin 60 =
3
2
tan 60 =
cos30 =
3
2
cos 60 =
cos 45 =
2
2
3
3
3
1
2
*these two problems will be done with no calculator, and will be done first…you will then hand in these
problems in exchange for the rest of the test