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: 75.8 , 51.9 , 36.2RST S R t
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
2
d > e
: 69.8 , 74.5, 21.3DEF D d e
The Side Opposite The Given Angle is Larger
is AcuteD
: 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
3
Using Stored Value in your Calculator
: 86 , 12, 13ABC A b c
Using Stored Value in your Calculator
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
4
: 61, 23, 47JKL j k l
: 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
117.0 , 0.1
19.6 , 0.1
43.3 , 0.1
J
K
L
5
150
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
220
150
The angle of depression
220
150
The angle of depression from the top of the lighthouse
220
370
The angle of depression from the top of the lighthouse
370
Is 14º
14º
14º
14ºx
Let x = the distance from the ship to the base of the cliff
370
370tan14
x
370
tan14x
1484ftx
6
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
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
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
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
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
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
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
286o
A
286o – 270o = 16o
286o
A
= 16o
56o
A
= 16o
56o
34o
A
= 16o
34o
34o
A
= 16o
34o
A
= 16o
34o
+ 34o
= 50o
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
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
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
7
K s s a s b s c
2
a b cs
semiperimeter
K s s m s n s p
2
m n ps
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
8
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:
1sin
2r sK Q
194 107 sin57
2K
: 57 , 94, 107QRS Q r s
Calculator Ready Form
4217.7
9
a vs b sin A
a < b
29 , 31, 23A b a
23 31 sin 29 15.03
is AcuteA
10
a vs b sin A
a < b
85 , 56, 48A b a
48 56 sin85 55.79
is AcuteA
11
b > a
132 , 96, 105B a b
The Side Opposite The Given Angle is Larger
is ObtuseB
12
j < k
141 , 36.1, 66J j k
The Side Opposite The Given Angle is Smaller
is ObtuseJ
13
m > n
41.2 , 83.2, 80.8M m n
The Side Opposite The Given Angle is Larger
is AcuteM
14
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
y z
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
siny vs z Y
si8 10 32nvs
8 5.299vs>
Y Z
8y
x
10z
X
: 32 , 8, 10XYZ Y y z
32
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
To The Nearest Tenth
: 32 , 8, 10XYZ Y y z
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
Y Z
8y 10z
X
32
Y Z
8y
x
10z
X
3241.5
x
: 32 , 8, 10XYZ Y y z
Y Z
8y 10z
X
32
Y Z
8y
x
10z
X
3241.5
x
: 32 , 8, 10XYZ Y y z
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
Y Z
8y 10z
X
32
Y Z
8y 10z
X
3241.5
138.5x x
: 32 , 8, 10XYZ Y y z
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
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
Y Z
8y
x
10z
X
32
Y Z
8y
c
10z
X
3241.5
138.5
106.5
14.5
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
106.5
14.5
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
41.5
138.5
9.5s in s ni X
x
Y
y
sin sin932
8
.5
x
9.58
3
in
n 2
s
six
2.5x 2.5
106.5
14.5
Y Z
8y
x
10z
X
32
Y Z
8y
x
10z
X
32
41.5
138.5
9.5
2.5
Y Z
8y
x
10z
X
32
138.5
9.5
2.5Y Z
8y
x
10z
X
32 41.5
106.5
14.5
15
218145
360
12 18 18sin145
2317.1in
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