Download Chapter 8: Trigonometry

CHAPTER 8: TRIGONOMETRY
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Title
Right Triangles + Magic = Trigonometry (DUE ON 2/5) – NO EXCEPTIONS!
Video: What is SOH CAH TOA?
SOH CAH TOA: The Set Up
Solving for a missing side
Solving for a missing angle
Connecting the dots of SOH CAH TOA
Video: Drawing and Word Problems
Drawing and Word Problems
Review
CHAPTER TEST
Complete?
February (2016)
3
4
Chp 7 Test
8
#3 Solving a
Missing Side/ #4
Solving a Missing
Angle
HW: Video #6
9
#5Connecting the
dots of SOH CAH
TOA
#7 Drawing and
Word Problems
5
#2 SOH CAH
TOA: The Set Up
HW: Right
Triangles+Magic=Trig #3 Solving a
Missing Side
Video #1
10
11
#7 Drawing and #8 Chapter Review
Word Problems
TEST
12
Name _________________________________
CC Geometry
Video: What is SOH CAH TOA?
Chp. 8 Wksht #1
SOH
CAH
TOA
The Sine Ratio (sin)
Opposite
sin  
Hypotenuse
The Cosine Ratio (cos)
Adjacent
cos  
Hypotenuse
The Tangent Ratio (tan)
Opposite
tan  
Adjacent
These ratios ONLY work in ______________ triangles!
Finding the opposite, adjacent and hypotenuse:
A
Angle A
Opposite =
Angle C
Opposite =
Adjacent =
Adjacent =
B
C
The Opposite and Adjacent sides ALWAYS depend on the _________________ ____________. The
hypotenuse is always located ______________ from the right angle.
Examples:
A
60o
5
1
3
B
30o
C
4
2
√𝟑
sin A=
sin B=
sin 30=
sin 60=
cos A=
cos B=
cos 30=
cos 60=
tan A=
tan B=
tan 30=
tan 60=
Solving for a missing side:
First, you must choose......
sin
cos
tan
Now, actually solve them......
Solving for a missing angle.....
sin
cos
tan
sin
cos
tan
Name _________________________________
CC Geometry
The Sine Ratio (sin)
Opposite
sin  
Hypotenuse
SOH CAH TOA: The Set Up
Chp. 8 Wksht #2
The Cosine Ratio (cos)
Adjacent
cos  
Hypotenuse
The Tangent Ratio (tan)
Opposite
tan  
Adjacent
1. Match the following.
a) _______ Opposite Leg to A
C
b) _______ Sine Ratio of C
c) _______ Opposite Angle to AB
B
A
d) _______ The Hypotenuse
1. A
e) _______ Adjacent Leg to A
BC
AC
8.
AB
AC
9.
BC
AB
2. B
f) _______ Tangent Ratio of C
BC
g) _______ Reference angle if
is the Cosine Ratio.
AC
h) _______ Adjacent Leg to C
3. C
4. AB
i) ________ Cosine Ratio of A
5. BC
j) ________ The Longest Side
k) _______ Reference angle if
7.
BC
is the Sine Ratio.
AC
10.
6. AC
AB
BC
2. Label the sides of the triangle using the reference angle -- (O) for Opposite, (A) for Adjacent and (H) for
Hypotenuse. After you have labeled the triangle, then choose which trigonometric ratio that you would use
to solve for the missing info.
a)
b)
c)
C
12 cm
x
29 cm
B
30°
C
A
A
B
x
d)
13°
A
21 cm
25 cm
B
θ
θ
C
34 cm
C
B
A
SIN
COS
TAN
e)
SIN
COS
TAN
f)
C
B
x
66°
SIN
COS
TAN
g)
A
18 cm
67°
12 cm
8 cm
B
B
x
x
C
A
TAN
SIN
COS
TAN
SIN
COS
TAN
63°
34 cm
B
COS
TAN
35°
C
A
SIN
COS
h)
C
x
SIN
25 cm
SIN
COS
A
TAN
Name _________________________________
CC Geometry
Solving for a missing side
Chp. 8 Wksht #3
Name _________________________________
CC Geometry
Solving for a missing angle
Chp. 8 Wksht #4
Name _________________________________
CC Geometry
Connecting the dots of SOH CAH TOA
Chp. 8 Wksht #5
1. A teacher asks (while looking at the trigonometry table), “What does the 0.6691 mean?” How would you
respond to that?
Degrees
42
Sine
0.6691
Cosine
0.7431
Tangent
0.9004
2. Thomas sees two triangles on the board in geometry class. From those he makes two claims:
CD EF

. How could he know this without having any
CB EG
numbers on the sides?
F
B
#1) that
C
24°
E
24°
D
G
CD
 0.9135, how could he know
CB
this without any numbers on the sides? What did he type into his calculator to get this value?
#2) that after clicking a couple of buttons on his calculator he states that
3. Sarah, the student who sits next to you in geometry class, notices that the values for sine and cosine are
only from 0 to 1 for the angles 0 to 90. She leans over and asks, “Why can’t sine and cosine be greater
than 1?” How would you respond to her?
4. A student who did very well in Algebra 1 looked at this trigonometry problem, and said “What a minute,
Tangent is the same as slope!!” Why would she says this? How is tangent the same as slope?
14 cm
θ
38 cm
5. Jessy claims that AB is the opposite side. Is he correct? Explain.
C
o
A
θ
B
6. What does similarity have to do with Trigonometry?
This stuff is IMPORTANT!
7. When looking closely at the trigonometry table a student notices that certain sine values are the same as
certain cosine values (partial table shown). What do the angles that have the same value have in common?
Degree
10
9
8
7
6
5
4
3
2
1
0
Sine
0.1736
0.1564
0.1392
0.1219
0.1045
0.0872
0.0698
0.0523
0.0349
0.0175
0.0000
Degree
80
81
82
83
84
85
86
87
88
89
90
Cosine
0.1736
0.1564
0.1392
0.1219
0.1045
0.0872
0.0698
0.0523
0.0349
0.0175
0.0000
8. Why does the sin Ɵ = cos (90 – Ɵ)?
9. Solve the following.
a) sin 42 = cos _______
d) cos 0 = sin _______

b) cos 12 = sin _______
c) sin 45 = cos _______
e) cos 65 = sin _______
f) sin 78.5 = cos _______
b) sin (2x – 17) = cos (x – 4)
3
1
c) sin ( x ) = cos ( x )
4
4
10. Solve for the unknown.
a) sin (x – 5) = cos (35)
Name _________________________________
CC Geometry
THE ANGLE OF ELEVATION
THE ANGLE OF DEPRESSION
Video: Drawing and Word Problems
Chp. 8 Wksht #6
Solve the given word problem.
1.
A 3.4 guy wire is attached to a tree 3
feet from the ground. What is the
angle that is formed between the wire
and the ground (to the nearest
degree)?
2.
A 15 feet ladder leans against a wall
at 52. How far from the wall is the
foot of the ladder (to the nearest
foot)?
3.
The sun’s ray strike the ground at 55,
21 m from the base of the tree. What
is the height of the tree (to the nearest
meter)?
4.
A little boy flies his kite. The string
formes an angle of elevation of 37
and from where he stands to directly
under the kite is 45 ft. How long is the
kite string (to the nearest ft)?
5.
A 10 feet ladder reaches a window
that is 8 feet up from the ground.
What is the angle that is formed
between the ladder and the wall (to
the nearest degree)?
6.
An airplane spots the floating debris at
an angle of depression of 15. If the
plane is at an altitude of 3,000 feet,
what is the horizontal distance before
they fly over it (to the nearest hundred
feet)?
Name _________________________________
CC Geometry
Drawing and Word Problems
Chp. 8 Wksht #7
1. Circle (or Draw) the side or angle that is represented by the description.
a) The Leaning Ladder
Height on the wall that
the ladder reaches.
b) The Leaning Ladder
The distance from
the foot of the ladder
to the wall.
e) Flying a Kite
c) The Leaning Ladder
The angle the ladder
forms with the wall.
d) The Shadow
The length of his shadow.
f) Flying a Kite
The length of the string.
The height of the kite.
What are some of the assumptions that are made about the kite example so that it works easily as a
trigonometry question?
g) The Support Guy Wire
h) The Support Guy Wire
The distance from the
base of the tree to where
the guy wire is fastened
to the ground.
The angle between the
antenna and the guy
wire.
i) The Support Guy Wire
The height of where the
guy wire is fastened
to the antenna.
j) The Support Guy Wire
The angle formed
between the wire
and the ground.
What are some of the assumptions that are made about the guy wire example so that it works easily as a
trigonometry question?
2. Create the diagram for the following descriptions. Label the diagram completely including putting the x for
the unknown missing value.
a) A young boy lets out 30 ft of string on his kite. If
the angle of elevation from the boy to his kite is 27°,
how high is the kite?
DIAGRAM
b) A 20 ft ladder leans against a wall so that it can
reach a window 18 ft off the ground. What is the
angle formed at the foot of the ladder?
DIAGRAM
c) To support a young tree, Jack attaches a guy wire
from the ground to the tree. The wire is attached to
the tree 4 ft above the ground. If the angle formed
between the wire and the tree is 70°, what is the
length of the wire?
DIAGRAM
d) A helicopter is directly over a landing pad. If Billy is
110 ft from the landing pad, and looks up to see the
helicopter at 65° to see it. How high is the
helicopter?
DIAGRAM
3. Solve the following problems. (All answers to 2 decimals places, unless otherwise instructed.)
a) A tree casts a shadow 21 m long. The angle of elevation of the sun is
55. What is the height of the tree?
b) You are flying a kite and have let out 30 ft of string but it got caught in
a 8 ft tree. What is the angle of elevation to the location of the kite?
c) A 15 m pole is leaning against a wall. The foot of the pole is 10 m from
the wall. Find the angle that the pole makes with the ground.
d) A lighthouse operator sights a sailboat at an angle of depression of 12.
If the sailboat is 80 m away, how tall is the lighthouse?
4. a) Using the drawbridge diagram, determine the distance from one side to the other. (exact answer)
45°
40 ft
45°
40 ft
b) Now that you know the distance from side to side, determine how high the drawbridge would be if the
angle of elevation was 60.(exact answer)
60°
60°
40 ft
c) How far apart would the drawbridge be if the angle of elevation of the drawbridge was 20?
x
20°
20°
For each problem, first draw the diagram and then solve for the requested information.
(All answers to 2 decimals places, unless otherwise instructed.)
5. An airplane is flying at an altitude of 6000 m over the ocean directly toward an island. When the
angle of depression of the coastline from the airplane is 14, how much farther does the airplane have
to fly before it crosses the coast?
6. A loading ramp is 25 m long with a height of 10 m. What is the horizontal distance of the ramp and
what is the angle of incline that the ramp forms with the ground?
7. A telephone pole casts a shadow 18 m long when the sun’s rays strike the ground at an angle of 70.
How tall is the pole?
For each problem, first complete the diagram and then solve for the requested information.
8. From an apartment window 24 m above the ground, the angle of depression of the base of a nearby
building is 38 and the angle of elevation of the top is 63. Find the height of the nearby building (to the
nearest meter).
24 m
9. A flagpole is at the top of a building. 400 ft from the base of the building, the angle of elevation of the
top of the pole is 22 and the angle of elevation of the bottom of the pole is 20. Determine the length of
the flagpole (to the nearest foot).
22°
20°
400 ft
10. From a lighthouse 1000 ft above sea level, the angle of depression to a boat (A) is 29. A little bit later
the boat has moved closer to the shore (B) and the angle of depression measures 44. How far (to the
nearest foot) has the boat moved in that time?
29°
44°
1000 ft
A
B
11. Jack and Jill are on either side of the church and 50 m apart. Jack sees the top of the steeple at 40 and
Jill sees the top of the steeple at 32. How high is the steeple?
h
32°
40°
50 m
12. Jack and Jill are 20 m apart. Jack sees the top of the building at 30 and Jill sees the top of the building
at 40. What is the height of building?
h
30°
20 m
40°
x
Name _________________________________
CC Geometry
Chapter Review
Chp. 8 Wksht #8
Vocabulary:
Sine
Cosine
Tangent
1. Which of the following is equal to cos 35
A) sin 35
B) cos 55
C) sin 55
D) cos 145
1. _________
2. If cos Ɵ = sin ß then which of the following must be true?
A) Ɵ + ß = 180 B) Ɵ - ß = 90
C) ß = 90Ɵ
D) ß - Ɵ = 90
2. _________
3. The angle of depression from the girl to the car is:
A) 1
B) 2
C) 3
D) 4
3. _________
4. Julie has a large red apple in her hand that is 4 ft off the
ground. A blue bird sees the apple at an angle of depression
of 55. If Julie is 15 ft from the tree, how tall is the tree
(round to the nearest foot)??
A) 16 ft
B) 17 ft
C) 21 ft
4. _________
D) 25 ft
5. A ladder reaches a window 12 ft above the ground and the foot of the
ladder is 4.8 ft from the wall. How long is the ladder?
A) 14 ft
B) 13 ft
C) 12 ft
5. _________
D) 11 ft
6. A lighthouse operator sights a sailboat at an angle of depression
of 25. If the lighthouse is 40 ft tall, how far is the boat from the
base of the lighthouse?
A) 95 ft
B) 86 ft
C) 44 ft
6. _________
d) 19 ft
7. Solve for the unknown.
a) sin (22)= cos (x)
b) sin (x + 18) = cos (45)
c) sin (2x – 15) = cos (x – 12)
8. A guy wire is attached to a tree 3.5 ft above the ground to stabilize it. If the guy wire
forms an angle with the tree of 50, what is the length of the guy wire? (2 decimal places)
9. A 15 ft ladder is leaning against a wall. The foot of the ladder is 4 ft from the wall.
Find the angle that the pole makes with the ground. (2 decimal places)
10. A man stands between two trees and he is 70 ft from the tall
tree and 50 ft from the shorter tree. If he sees the taller tree at an
angle of 38 and the smaller at 45 , what is the difference in the
heights of the two trees (to the nearest foot) ?
11. Two bird watchers position themselves at point A (the beach) and
point C (the shed) which are 111 ft apart. The both spot the rare Blue
Breasted Turk at point B using their binoculars. If they see the Blue
Breasted Turk at 94 and 46 respectively, how far is the bird from the
bird watcher in the shed (point C) (round to the nearest ft)?
B
46°
A
12. Some marine biologists are studying rare red belly salmon in the
north portion of the lake. They have gathered some of the
measurements of the area but still need to determine the width (from A
to B) of the north portion of the lake. Determine the width of the north
lake (from A to B) to the nearest foot.
94°
111 ft
B
178 m
53° C
589 ft
A
C