Trig Ratios

1
Trig Ratios

• And other
• formulas

2
Right Triangle Trigonomety

• By Jeffrey Bivin
• Lake Zurich High School
• jeff.bivin_at_lz95.org

Last Updated November 14, 2010
3
SOH CAH TOA
hypotenuse
opposite
?
adjacent
4
Reciprocal Identities
hypotenuse
opposite
?
adjacent
5
Reciprocal Identities
hypotenuse
opposite
?
adjacent
6
Reciprocal Identities
hypotenuse
opposite
?
adjacent
7
Find the sides.
B
2
c
a
1
A
C
b
8
Find the sides.
B
c
a
10
A
C
b
9
Find the sides.
B
c
a
17
A
C
b
10
Find the sides.
B
c
a
1
A
C
b
1
11
Find the sides.
B
c
a
A
C
b
9
12
Find the sides.
Use your calculator!
B
15
68o
c
a
22o
A
C
b
13
Find the sides.
B
56o
c
a
25
34o
A
C
b
14
Find the angles and the 3rd side.
25
ß
?
21
15
Find the angles and the 3rd side.
ß
6
?
11
16
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17
Pythagorean Identities
hypotenuse
opposite
?
adjacent
18
Pythagorean Identities

• Find cos? if sin?

19
Pythagorean Identities

• Find sec? if tan?

20
Pythagorean Identities

• Find sin? if cot?

21
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22
Law of Sines
B
a
c
C
A
b
23
Law of Sines
B
a
c
12
82o
C
25o
A
b
24
Law of Sines
B
a
73o
c
12
82o
C
25o
A
b
180 - (8225) 73o
a 5.121 B 73o b 11.588
25
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26
Law of Sines
B
a
105o
9
c
55o
C
20o
A
b
180 - (10555) 20o
27
Law of Sines
B
a
105o
9
c
55o
C
20o
A
b
A 20o b 25.417 c 21.555
28
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29
Law of Sines
B
a
17
18
c
C
63o
A
b
When finding an angle using Law of Sines, two
possibilities exist.
30
Law of Sines
B
a
17
18
c
46.366o
70.634o
C
63o
A
b
Triangle 1
B 180 - (6370.634) 46.366o
31
Law of Sines
B
a
17
18
c
7.634o
109.366o
C
63o
A
b
Triangle 2
B 180 - (63109.366) 7.634o
32
Law of Sines
B
a
17
18
c
C
63o
A
b
Triangle 2
Triangle 1
C 70.634o B 46.366o b 13.809
C 109.366o B 7.634o b 2.535
33
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34
Law of Sines
B
a
15
25
c
65o
C
A
b
When finding an angle using Law of Sines, two
possibilities exist.
35
Law of Sines
B
a
15
25
c
65o
C
32.942o
A
b
Option 1
B 180 - (6532.942) 82.058o
36
Law of Sines
B
a
15
25
c
65o
C
147.058o
A
b
Option 2
Not a Triangle
B 180 - (65147.058) -32.058
37
Law of Sines
B
a
15
25
c
65o
C
32.942o
A
b
A 32.942o B 82.058o b 27.320
38
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39
Law of Cosines
B
a
c
5
C
25o
A
b
8
40
Law of Cosines
B
a 4.061 B 123.659o C 31.341o
4.061
a
c
5
C
25o
A
b
8
41
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42
Law of Cosines
B
8
a
c
13
C
A
b
20
43
Law of Cosines
B
A 14.795o B 143.406o C 22.799o
8
a
c
13
C
A
b
20