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1
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: 75.8 , 51.9 , 36.2RST S R t
![Page 4: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/4.jpg)
52.3 , 36, 44.4T r s
180 75.8 51.9 52.3T
51.936. sin
si
2
2.3n5r
Calculator Ready Forms
75.836. sin
si
2
2.3n5s
: 75.8 , 51.9 , 36.2RST S R t
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2
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d > e
: 69.8 , 74.5, 21.3DEF D d e
The Side Opposite The Given Angle is Larger
is AcuteD
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: 69.8 , 74.5, 21.3DEF D d e
180 69.8 15.6 15.6F
94.674. sin
si
5
9.8n 6f
Calculator Ready Forms
sin 6sin
21.3
74.5
9.8E
15.6 , 94.6 , 79.1E F f
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3
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Using Stored Value in your Calculator
: 86 , 12, 13ABC A b c
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Using Stored Value in your Calculator
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44.5 , 49.5 , 17.1B C a
180 86 44.5 49.5C
sinsin is the stored value
86of
12, side
AAB a
Calculator Ready Forms
2 212 13 2 12 13 cos86a
: 86 , 12, 13ABC A b c
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4
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: 61, 23, 47JKL j k l
![Page 14: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/14.jpg)
: 61, 23, 47JKL j k l
Calculator Ready Forms
2 2 247 23
cos61
2 47 23J
2 2 247 61
cos23
2 47 61K
2 2 223 61
cos47
2 23 61L
Use any 2 of the below and find the third by subtraction
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117.0 , 0.1
19.6 , 0.1
43.3 , 0.1
J
K
L
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5
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150
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
220
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150
The angle of depression
220
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150
The angle of depression from the top of the lighthouse
220
370
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The angle of depression from the top of the lighthouse
370
Is 14º
14º
14º
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14ºx
Let x = the distance from the ship to the base of the cliff
370
370tan14
x
370
tan14x
1484ftx
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6
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A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
56o
460
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A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
460 x 3
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A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o
460
![Page 26: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/26.jpg)
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
460 460 x 2
![Page 27: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/27.jpg)
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
A
B
C
a
b
c460
![Page 28: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/28.jpg)
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
A
B
C
a
b
c
2 2 2 2 cosa b c bc A= + -
460
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460
138056o
286o920
A
B
C
a
b
c
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
![Page 30: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/30.jpg)
286o
A
286o – 270o = 16o
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286o
A
= 16o
56o
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A
= 16o
56o
34o
![Page 33: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/33.jpg)
A
= 16o
34o
34o
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A
= 16o
34o
![Page 35: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/35.jpg)
A
= 16o
34o
+ 34o
= 50o
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A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
A
B
C
a
b
c
2 2 2 2 cosa b c bc A= + -
= 50o
460
![Page 37: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/37.jpg)
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
A
B
C
a
b
c
( )( )2 2 21380 920 2 1380 920 cos50a = + - o
= 50o
460
![Page 38: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/38.jpg)
A plane leaves an airport at a heading of 56° and a speed of 460 mph, after three hours it changes to a heading of 286°.
After 2 more hours how far will it be from the airport? Draw a diagram.
460
138056o
286o920
A
B
C
a
b
c
1057.6a=
= 50o
460
![Page 39: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/39.jpg)
7
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K s s a s b s c
2
a b cs
semiperimeter
![Page 41: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/41.jpg)
K s s m s n s p
2
m n ps
![Page 42: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/42.jpg)
65.5 65.5 661 235.5 65. 475K
61 23 47
265.5s
: 61, 23, 47MNP m n p
Calculator Ready Form
481.4
![Page 43: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/43.jpg)
8
![Page 44: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/44.jpg)
1sin
2bcK A
1sin
2acK B
1sin
2abK C
Given 2 sides and the included angle, the area of a triangle can be given by any one of the following formulas:
![Page 45: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/45.jpg)
1sin
2r sK Q
![Page 46: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/46.jpg)
194 107 sin57
2K
: 57 , 94, 107QRS Q r s
Calculator Ready Form
4217.7
![Page 47: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/47.jpg)
9
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a vs b sin A
a < b
29 , 31, 23A b a
23 31 sin 29 15.03
is AcuteA
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10
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a vs b sin A
a < b
85 , 56, 48A b a
48 56 sin85 55.79
is AcuteA
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11
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b > a
132 , 96, 105B a b
The Side Opposite The Given Angle is Larger
is ObtuseB
![Page 53: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/53.jpg)
12
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j < k
141 , 36.1, 66J j k
The Side Opposite The Given Angle is Smaller
is ObtuseJ
![Page 55: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/55.jpg)
13
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m > n
41.2 , 83.2, 80.8M m n
The Side Opposite The Given Angle is Larger
is AcuteM
![Page 57: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/57.jpg)
14
![Page 58: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/58.jpg)
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
![Page 59: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/59.jpg)
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
y z
![Page 60: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/60.jpg)
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
siny vs z Y
si8 10 32nvs
8 5.299vs>
![Page 61: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/61.jpg)
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
Y Z
8y
x
10z
X
32
![Page 62: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/62.jpg)
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
To The Nearest Tenth
: 32 , 8, 10XYZ Y y z
![Page 63: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/63.jpg)
Y Z
8y
x
10z
X
32
Y Z
8y
c
10z
X
32
sin sinY Z
y z
32
8
si
10
n sin Z
10 32
8
sinsin Z
To The Nearest Tenth
41.5Z
![Page 64: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/64.jpg)
Y Z
8y 10z
X
32
Y Z
8y
x
10z
X
3241.5
x
: 32 , 8, 10XYZ Y y z
![Page 65: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/65.jpg)
Y Z
8y 10z
X
32
Y Z
8y
x
10z
X
3241.5
x
: 32 , 8, 10XYZ Y y z
![Page 66: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/66.jpg)
Y Z
8y 10z
X
32
Y Z
8y 10z
X
3241.5
180 41.5 138.5
138.5x x
: 32 , 8, 10XYZ Y y z
![Page 67: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/67.jpg)
Y Z
8y 10z
X
32
Y Z
8y 10z
X
3241.5
138.5x x
: 32 , 8, 10XYZ Y y z
![Page 68: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/68.jpg)
Y Z
8y 10z
X
32
Y Z
8y
c
10z
X
3241.5
138.5
180 ZX Y
32 4180 1.5X
106.5X
106.5
x
![Page 69: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/69.jpg)
Y Z
8y
x
10z
X
32
Y Z
8y
c
10z
X
3241.5
138.5
s in s ni X
x
Y
y
sin si 1032
8
n 6.5
x
106.5
106.58
32
sin
sinx
14.5x
14.5
![Page 70: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/70.jpg)
Y Z
8y
x
10z
X
32
Y Z
8y
c
10z
X
3241.5
138.5
106.5
14.5
![Page 71: 1 Calculator Ready Forms 2 d > e The Side Opposite The Given Angle is Larger](https://reader035.vdocuments.net/reader035/viewer/2022062714/56649d035503460f949d6a12/html5/thumbnails/71.jpg)
106.5
14.5
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
41.5
138.5
180 ZX Y
32 1180 38.5X
9.5X
9.5
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