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The word trigonometry means “triangle
measurement.” You can use trigonometry to
calculate the lengths of sides and the measures
of angles in triangles.
Trigonometry has been used for centuries in the study of:
surveying
astronomy
engineering
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geography
physics
B
opposite
A
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adjacent
C
B
adjacent
A
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opposite
C
B
opposite
A
opp
sin A 
hyp
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adjacent
adj
cos A 
hyp
C
opp
tan A 
adj
B
adjacent
A
opp
sin B 
hyp
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opposite
adj
cos B 
hyp
C
opp
tan B 
adj
B
opp
A
adj
C
SOH CAH TOA
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SOH
CAH
TOA
B
hy
p
10
A
8
op
p
C
6
adj
8
sin A 
10
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6
cos A 
10
8
tan A 
6
B
SOH
CAH
TOA
hy
p
5
adj
A
12
sin B 
13
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12
opp
5
cos B 
13
C
12
tan B 
5
Example 1: Determine side b
SOH
CAH
TOA
b
tan B 
8
b
tan 55 
8
55º
8 cm
A
b = 8 tan 55°
b = 11.4 cm
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B
ad
C j
b
opp
Example 2: Determine side c
if A is 31°.
13
cos 31 
c
13
c
cos31
c = 15.2
B
hyp
A
13 cm
C
ad
j
SOH
CAH
TOA
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Example 3: Determine side p if P is 45°.
p
sin 45 
17
R
p  17(sin 45 )
Q
p = 12.0
SOH
CAH
TOA
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P
Ex. 4: From a distance of 20 m from the base a
lighthouse the angle of elevation to the top of a
lighthouse is 38º. Determine the height of the
lighthouse.
h
tan 38 
20
h = 20 tan 38°
h = 20 (0.7813)
hh
38º
20 m
h = 15.6
The lighthouse is 15.6 m high.
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