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Finding a
Finding a
missing
Trig ratios missing side angle
Word
Problems
Sec, csc,
and cot
100
100
100
100
100
200
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500
Category 1
100
Identify the hypotenuse,
adjacent and opposite sides.
Reference Angle C
A
B
C
Category 1
100
A
Opposite
B
Hypotenuse
Adjacent
C
Category 1
200
What does SOH-CAH-TOA
mean?
Category 1
200
Sine
Opposite over Hypotenuse
Cosine
Adjacent over Hypotenuse
Tangent
Opposite over Adjacent
Category 1
300
Write the following Trig
ratio:
Cos A
12
C
A
20
16
B
Category 1
300
Cos A = 12/20 = 3/5
12
C
A
20
16
B
Category 1
400
Write the following Trig
ratio:
Y
Tan X
16
Z
12
20
X
400
Category 1
Tan X = 16/12 = 4/3
Y
16
Z
12
20
X
500
Category 1
Write the following Trig
ratios: sin A, cos A, tan A
39
A
B
15
36
C
500
Category 1
sin A = 15/39 = 5/13
cos A = 36/39 = 12/13
tan A = 15/36 = 5/12
39
A
B
15
36
C
100
Category 2
Find the missing Side.
Found to the nearest
tenth.
x
72o
5
Category 2
100
x = 16.2
Category 2
200
Find the missing Side.
Found to the nearest
tenth.
x
24o
12
Category 2
200
x = 5.3
Category 2
300
Find the missing Side.
Found to the nearest
tenth.
14
x
49o
Category 2
300
x = 12.2
400
Category 2
Find the missing Side.
Found to the nearest
tenth.
14
51o
x
Category 2
x = 18.0
400
Category 2
500
Find the missing Side.
Found to the nearest
tenth.
x
21
65o
Category 2
500
x = 52.0
Category 3
100
Find the missing angle.
Found to the nearest
degree.
42
?
40
Category 3
100
o
72
200
Category 3
Find the missing angle.
Found to the nearest
degree.
27
?
11
Category 3
200
o
24
Category 3
300
Find the missing angle.
Found to the nearest
degree.
13
20
?
Category 3
300
o
49
Category 3
400
Find the missing angle.
Found to the nearest
degree.
12
?
24
Category 3
400
o
30
Category 3
500
Find the missing angle.
Found to the nearest
degree.
51
?
68
Category 3
500
53o
Category 4
100
A 15-foot ladder is leaning
against a wall creating a
36o angle. How high up the
wall does the ladder reach?
Category 4
x = 12.1 feet
100
Category 4
200
A ship is approaching a lighthouse
with a sailor on its bow. The sailor
is looking at the top of the
lighthouse with a range finder.
The top of the lighthouse is 500
yards away at an angle of 18˚. How
far is the ship away from the
lighthouse?
Category 4
475.5 yards
200
Category 4
300
A pine tree sits in a clearing. It
casts a 45 foot shadow on the
ground. The angle from the end
of the shadow to the top of the
tree is 40˚. How tall is the
tree?
Category 4
37.8 feet
300
Category 4
400
A boy flying a kite lets out 300
feet of string which makes an
angle of 38o with the ground.
Assuming that the string is
straight, how high above the
ground is the kite.
Category 4
184.7 feet
400
Category 4
500
An airplane climbs at an angle of
elevation 11o with the ground.
Find the ground distance it has
traveled when it has attained an
altitude of 400 feet.
Category 4
2057.8 feet
500
Category 5
100
Cosecant A is the reciprocal
in of which trigonometric
function?
Category 5
Sine A
Csc A = 1/sin A
100
Category 5
200
Cotangent A is the reciprocal
in of which trigonometric
function?
Category 5
Tangent A
Cot A = 1/tan A
200
Category 5
300
Secant A is the reciprocal in
of which trigonometric
function?
Category 5
Cosine A
Sec A = 1/cos A
300
400
Category 5
What are two ratios we could
use to represent the following
ratio: a/b
A
c
B
b
a
C
Category 5
Sin A = Cos C = a/b
400
500
Category 5
What are two ratios we could
use to represent the following
ratio: c/a
A
c
B
b
a
C
Category 5
Tan C = Cot A = c/a
500