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Test Review – Geometry Unit 7:
1. Special Right Triangles:
Find the missing sides of each triangle
a)
b)
6
c)
20
8
30°
30°
d)
e)
30°
f)
15
30°
30°
30°
12
g)
h)
i)
12
8
45°
45°
j)
c
10
b
a
45°
30°
d
e
18
6 3
45°
2. Right Triangle Trigonometry (SOH-CAH-TOA)
b)
c)
50
°
a)
12
x
x
d)
°
20
10°
e)
f)
10
x
x
16
70°
20°
14
x
°
40
i)
10
h)
12
g)
4
6



2
j)
15
10
x
4
k)
l)
2

6
18
24
5
8


3. Angle of elevation and depression:
See the word problems skipped in our original packet for
extra practice.
4. Exact values:
1) (sin 45°)(cos 30°)
2) (sin 45°)(cos 60°)
3) (sin 30°)+ (cos 60°) + (tan 45°)
4) (cos 45°)(tan 30°)
5) (sin 60°)(tan 60°)
5. Cofunctions:
1) sin (7x + 2)° = cos (3x + 5)°
2) sin (8x + 12)° = cos (7x + 3)°
3) sin (2x)° = cos (8x)°
6. Law of sines:
A ship is traveling toward a lighthouse. It measures the angle of
elevation to the top of the lighthouse to be 10°. It travels 300 feet
closer and measures the angle of elevation to be 20°. Find how far
from the lighthouse the ship is when the second angle of elevation is
measured.
See the next page for additional law of sines practice.
Law of Sines Continued:
a) The diagram below shows the plans for
a cell phone tower. A guy wire attached
to the top of the tower makes an angle
of 65 degrees with the ground. From a
point on the ground 100 feet from the
end of the guy wire, the angle of
elevation to the top of the tower is 32
degrees. Find the height of the tower, to
the nearest foot.
b) A ship at sea heads directly toward a
cliff on the shoreline. The
accompanying diagram shows the top of
the cliff, D, sighted from two locations,
A and B, separated by distance S. If
,
, and
,
what is the height of the cliff, to the
nearest foot?
c) A sign 46 feet high is placed on top of
an office building. From a point on the
sidewalk level with the base of the
building, the angle of elevation to the
top of the sign and the angle of
elevation to the bottom of the sign are
40° and 32°, respectively. Sketch a
diagram to represent the building, the
sign, and the two angles, and find the
height of the building to the nearest
foot.
d) While sailing a boat offshore, Donna
sees a lighthouse and calculates that the
angle of elevation to thetop of the
lighthouse is 3°, as shown in the
accompanying diagram. When she sails
her boat 700 feet closer to the
lighthouse, she finds that the angle of
elevation is now 5°. How tall, to the
nearest tenth of a foot, is the
lighthouse?