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Lesson 13.1
Right Triangle Trigonometry

Adjacent Leg
SOH
opp
sin  
hyp
hyp
1
csc  

opp sin 
CAH
adj
cos  
hyp
hyp
1
sec  

adj cos 
TOA
opp
tan  
adj
cot  
adj
1

opp tan 
Finding Exact Values
30-60-90
60°
2
1
30°
3
sin 30 
1
2
3
cos 30 
2
tan 30 
1
3

3
3
3
sin 60 
2
1
cos 60 
2
tan 60 
3
Finding Exact Values
1
45°
45-45-90
2
2
45°
2
45°
45°
1
2
sin 45 
2
2
2
cos 45 
2
tan 45 
2
1
2
Example 1
Find Trigonometric Values
[A]

3
5
4
4
sin  
5
5
csc 
4
3
cos 
5
5
sec 
3
4
tan  
3
3
cot  
4
Example 1
Find Trigonometric Values
[B]
13
5

12
5
sin  
13
13
csc 
5
12
cos 
13
13
sec 
12
5
tan  
12
12
cot  
5
Example 2
[A]
Use one Trig Ratio to find others
2
cos 
5
cot   ?

Example 2
[B]
Use one Trig Ratio to find others
5
tan  
3
sec   ?
34

3
hyp
34
sec  

adj
3
32  5 2  h 2
34  h 2
h  34
5
Example 3
Find missing sides of Right Triangles
Calculator Free
[A]
SOH
CAH
TOA
8
30°
x
Example 3
[B]
60°
Find missing sides of Right Triangles
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x
12
SOH
CAH
TOA
12
sin 60 
x
3 12

2
x
x 3  24
24
x
3
24 3
x
8 3
3
Example 3
Find missing sides of Right Triangles
Calculator Free
[C]
45°
x
12
SOH
CAH
TOA
Example 3
Find missing sides of Right Triangles
Calculator Free
[D]
45°
10
x
SOH
CAH
TOA
x
sin 45 
10
2 x

2 10
2 x  10 2
x 5 2
Example 4 Solve a Triangle
Solve triangle ABC. Round lengths to the nearest tenth.
C
10
Angles
A=
B=
C=
35°
A
B
Sides
a=
b=
c=
Example 5 Solve a Triangle with Missing Angle
Solve triangle ABC. Round lengths to the nearest tenth.
C
5
A
12
B
Angles
A=
B=
C=
Sides
a=
b=
c=
Example 6
Angle of Elevation and Depression
Line of Sight

  Angle of Depression
  Angle of Elevation

Line of Sight