8-4 Trigonometry
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Transcript 8-4 Trigonometry
D.N.A.
Find the missing sides of the special right triangles.
1)
7 3
2)
30
45 12
45
3) Solve
for x.
19
x
60
11
Complete your DNA on a
fresh sheet of paper. Label
it as shown on the board.
Chapter 8-4
Trigonometry
• trigonometry
• Find trigonometric ratios
using right triangles.
• Solve problems using
trigonometric ratios.
• trigonometric ratio
• sine
• cosine
• tangent
Standards 18.0 Students know the definitions of the basic
trigonometric functions defined by the angles of a right
triangle. They also know and are able to use elementary
relationships between them. For example, tan(x) =
sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. (Key)
Standards 19.0 Students use trigonometric functions to
solve for an unknown length of a side of a right triangle,
given an angle and a length of a side. (Key)
The Amazing Legend of…
Chief
SohCahToa
Chief SohCahToa
• Once upon a time there was a wise old Native
American Chief named Chief SohCahToa.
• He was named that due to an chance encounter
with his coffee table in the middle of the night.
• He woke up hungry, got up and headed to the
kitchen to get a snack.
• He did not turn on the light and in the darkness,
stubbed his big toe on his coffee table….
opposite side
Sine(Sin)
S
o:h
hypotenuse
adjacent side
Cosine (Cos)
C
a:h
hypotenuse
opposite side
Tangent(Ta n)
B
adjacent side
T o:a
Opposite
Side
A
Adjacent
Side
C
Find Sine, Cosine, and Tangent Ratios
Find sin L, cos L, tan L, sin N, cos N,
and tan N. Express each ratio as a
fraction and as a decimal. S o : h C a : h
L
8 : 17 15 : 17
Hypotenuse
15
8
17
17
T o :a
8 : 15
Adjacent
8
15
Find Sine, Cosine, and Tangent Ratios
Find sin L, cos L, tan L, sin N, cos N,
and tan N. Express each ratio as a
fraction and as a decimal.
Ca:h
N
Hypotenuse
S o:h
15 : 17
Adjacent
15
17
8 : 17
8
17
To:a
15 : 8
15
8
Find Sine, Cosine, and Tangent Ratios
Answer:
A. Find sin A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
B. Find cos A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
C. Find tan A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
D. Find sin B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
E. Find cos B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
F. Find tan B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Using a Trig. Table
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Angle
Measure
10
26
Sin Cos
Tan
Angle
Measure
Sin
Cos
10
56
26
72
Tan
.1736 .9848 .1763
56
.8290 .5592 1.483
.4877
72
.9511 .3090 3.077
.4384 .8988
A. Use your trig. table to find sin 48° to the nearest
ten thousandth.
A. 0.6691
B. 1.1106
C. 0.7431
D. 0.7314
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
B. Use your trig. table to find cos 85° to the nearest
ten thousandth.
A. 0.0872
B. 0.9962
C. 11.4301
D. 0.0698
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Use Trigonometric Ratios to Find a Length
EXERCISING A fitness trainer sets the incline on a
treadmill to 7°. The walking surface is 5 feet long.
Approximately how many inches did the trainer raise
the end of the treadmill from the floor?
=60 in
Let y be the height of the
treadmill from the floor in
inches. The length of the
treadmill is 5 feet, or 60 inches.
opposite
sin 7
hypotenuse
y
.1219
60
y
60(.1219) 60
60
y =7.314 in
Answer: The treadmill is about 7.3 inches high.
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
the ramp is about 4.8°, how high does the ramp rise
off the ground to the nearest inch?
A. 1 in.
B. 11 in.
C. 16 in.
1.
2.
3.
4.
D. 15 in.
0%
A
B
C
D
A
B
C
D
Use Trigonometric Ratios to Find an
Angle Measure
COORDINATE GEOMETRY Find mX in right ΔXYZ
for X(–2, 8), Y(–6, 4), and Z(–3, 1).
XY 4 4 32 4 2
2
4 2
XZ 72 12 50 5 2
5 2
3 2
2
YZ 32 32 18 3 2
Use Trigonometric Ratios to Find an
Angle Measure
COORDINATE GEOMETRY Find mX in right ΔXYZ
for X(–2, 8), Y(–6, 4), and Z(–3, 1).
XY 4 2 5.656
5.46562
37
57.071
2
3 243
2
4.
XZ 5 2 7.071
YZ 3 2 4.243
Opposite
4.243
SinX
0.6
Hypotenuse 7.071
mX 37 from trig.
table
COORDINATE GEOMETRY Find mA in right ΔABC
to the nearest degree.
A. 66.0°
B. 56.3°
C. 33.7°
D. 24.0°
A.
B.
C.
D.
A
B
C
D
Homework
Chapter 8-4
• Pg 460:
# 1, 2, 10, 11,
14 – 17 all, 26,
29 – 49 odd