Transcript Trigonometry

Trigonometry
Chapter 6
Sections 16-20
“Yeah!!!! We can use calculators!!!”
“Measurement of triangles”
Sine ~ Cosine ~ Tangent
• Sine, cosine and tangent are ratios that exist in
right triangles.
• The ratio of two sides of any right triangle with
the same interior angles is always the same
number independent of the size of the triangle.
• They are abbreviated as Sin, Cos, and Tan
3
31 °
5
6
31 °
10
12
31 °
20
SOHCAHTOA
• Sin =
Opposite
Hypotenuse
• Cos =
Adjacent
Hypotenuse
• Tan =
Opposite
Adjacent
SOHCAHTOA
•
Sin A = O =
H
•
Cos A = A =
H
4
5
3
5
•
•
Tan A = O =
A
4
3
A
5
3
A
C
4
H
O
B
SOHCAHTOA
Sin A = O = 4 •
Sin B = O =
3
5
5
H
3
Cos A = A =
• Cos B = A = 4
5
H
H 5
H
•
Tan A = O =
A
4 • Tan B = O = 3
3
4
A
A
5
3
O
C
4
H
A
What is the relationship between Sin A° & Cos B? Tan A° and Tan B °?
Sin A° =
Cos B°
b/c A ° & B ° are
Cos A° =
Sin B°
Complementary ’s
Tan A° and Tan B °are reciprocals.
B
Using the chart
page 771
•
• Examples
O
3
Tan 31° =
= =
A
5
.6
• sin 28° = x
• cos 88°= x
•
O
Tan 31° =
A
6
= = .6
10
• Cos A = .3746
• Sin B = .6018
3
31 °
5
6
31 °
10
12
31 °
20
Using a calculator
•
When you turn on your calculator ,
check to see if Deg appears on the screen
•
If not, hit DRG
•
To find the Sin, Cos, or Tan of any degree measure:
•
button until Deg appears.
Find Sin 30° - Hit 3
0
SIN
Sin 30° = .5 or ½ - Hit
•
Find Cos 30° - Hit 3
0
COS
Cos 30 ° = .866025404 or
•
3
2
We always round to 4 decimal places, so Cos 30° = .8660
Using a calculator
•
To show that tangents are reciprocals of each
other using the calculator:
•
Find Tan 30° 3
0
TAN
•
You will get .577350269
•
Take the reciprocal of this using 1/x
•
You will get 1.73205080
•
How do you find what angle this is the tangent of ?
Do SOCAHTOA Tri Probs 2
Angle of Elevation
•
READ PAGE 336
HORIZONTAL LINE
Angle of Depression
•
READ PAGE 336
HORIZONTAL LINE
ANGLE OF
DEPRESSION
Trig Word Problems
Steps
• Locate the  in the problem
• Label sides according to the 
• Decide which trig ratio to use
• Substitute
• Solve
Examples
1. From the top of a lighthouse 160 feet above
sea level, the angle of depression of a boat at
sea contains 35°. Find to the nearest foot the
distance from the boat to the foot of the
lighthouse.
35°
55°
160
x
Examples
2. Find to the nearest degree the measure of
the angle of elevation of the sun when a
vertical pole 6 feet high casts a shadow 8 feet
long.
6
x
8
Examples
3. A boy who is flying a kite lets out 300 feet
of string which makes an angle of 38° with the
ground. Assuming that the string is straight,
how high above the ground is the kite? Give
your answer to the nearest foot.
300
38°
x
Examples
4. A plane took off from a field and rose at an
angle of 8° with the horizontal ground. Find to
the nearest ten feet the horizontal distance the
plane has covered when it has flown 2000 feet.
2000
8°
x
Examples
5. A road is inclined 8° to the horizontal. Find to
the nearest hundred feet the distance one must
drive up this road to increase one’s altitude 1000
feet.
Examples
6. A wire reaches from the top of a telephone
pole to a stake in the ground. The stake is 10 feet
form the foot of the pole. The wire makes an
angle of 65° with the ground. Find to the nearest
foot the length of the wire.
Examples
A 40 feet ladder which is leaning against a
wall reaches the wall at a point 36 feet from
the ground. Find to the nearest degree the
number of degrees contained in the angle
which the ladder makes with the wall.