Download no.12 Notes slides ch.13

#12 Opener
Solutions
#1
A squirrel drops a nut from a tree. The nut
would normally drop 15 feet vertically, but
because of the wind it travels along a path
that forms a 17º angle with the vertical. How
far from the tree does that nut land? (Round
to the nearest hundredth.)
17º
15 feet
x
4.59 feet
#2
A television antenna sits atop
a building. From a point 150
feet away from the base of
the building, the
measurement of the angle of
elevation to the top of the
antenna is 75º. From the
same point, the measurement
of the angle of elevation to
the bottom of the antenna is
68º. How tall is the antenna?
tan 75 =
x+ y
150
x = antenna
75º
Whole
Angle
y= building
68º
150 feet
y
and tan 68 =
150
189 feet
#12
Notes / Review
Chapter 13
#6-#11
Doors vs. Windows
One person from each team
will be called on.
If correct, 1 goodie from the
Amazing Bag of Goodies
and 3 bean bag tosses.
Bean Bag Toss
3 tosses each
3 points for in the hole
2 points for leaning over the hole
1 point for on the box
**Clean up after yourself when
you are done.
Grade Book
Winning team = 6/5 in grade book
2nd place = 5/5 in grade book
Target Goal:
The students will be able
to use right triangles to find
trigonometric values and
solve problems involving
right triangles using right
triangle trigonometry.
#1
Solve the right triangle.
(Draw a picture.)
a = 11 inches
b = 22.3 inches
(Round to the nearest tenth.)
c = 24.9 inches
A = 26.3º
B = 63.7º
Target Goal:
The students will be able
to use right triangles to find
trigonometric values and
solve problems involving
right triangles using right
triangle trigonometry.
#2
Solve the right triangle.
(Draw a picture.)
A = 22º
c = 42 meters
B = 68º
a = 15.7 meters
b = 38.9 meters
#3
Target Goal:
The students will be able to
solve word problems using
right triangle trigonometry.
Application:
Show all work.
Dave is 200 feet away from a
tower and he has determined the
angle of elevation to the top of the
tower to be 32º. Find the height of
the tower to the nearest foot.
x
32º
200
tan 32 =
x
200
125 feet
#4
Target Goal:
The students will be able to
solve word problems using
right triangle trigonometry.
Application:
Show all work.
Two cities are 10 miles apart. An
object is seen hovering in the sky
above the line joining the two
cities. The angles of elevation from
the cities to the object are 24º and
40º. What is the height of the
object above the ground?
(Round to the nearest tenth.)
* object
x
40º
10-a
a
24º
* object
x
40º
tan 24 =
10-a
x
a
a
and tan 40 =
24º
x
10−a
2.9 miles
#5 Application:
Target Goal:
The students will be able to
solve word problems using
right triangle trigonometry.
(Show all work.)
A man is in a boat that is
floating 175 feet from the base
of a 200 foot cliff. What is the
angle of depression between the
cliff and the boat? Round to the
nearest tenth.
tan x
200
= 175
x
200 feet
x
175 feet
48.8º
Target Goal:
The students will be able to find
values of trigonometric
functions for general angles.
#6
The terminal side of θ in standard
position contains the point (8, 4).
Find the exact values of the six
trigonometric functions of θ .
sinθ = 5
5
cosθ = 2 5
5
tanθ = 1
2
cscθ = 5
secθ = 5
2
cotθ =2
Target Goal:
#7
The students will be able to find
values of trigonometric
functions for general angles.
The terminal side of θ in standard
position contains the point (8, -15).
Find the exact values of the six
trigonometric functions of θ .
sinθ =−15
17
cosθ = 8
17
tanθ =−15
8
cscθ =−17
15
secθ = 17
8
cotθ =− 8
15
Target Goal:
#8
The students will be able to find
values of trigonometric
functions for general angles.
The terminal side of θ in standard
position contains the point (-4, -3).
Find the exact values of the six
trigonometric functions of θ .
sinθ =− 3
5
cscθ =− 5
3
cosθ =− 4
5
secθ =− 5
4
tanθ = 3
4
cotθ = 4
3
Target Goal:
#9
The students will be able to find
values of trigonometric
functions for general angles.
The terminal side of θ in standard
position contains the point (0, 10).
Find the exact values of the six
trigonometric functions of θ .
sinθ =1
cosθ =0
cscθ =1
secθ =undefined
tanθ =undefined
cotθ =0
Target Goal:
#10
The students will be able to find
values of trigonometric
functions by using reference
angles.
• Sketch a 135º angle.
• Name the reference angle.
• Put the correct proportions for the
reference angle.
• Find the exact value for the
sin 135º and tan 135º.
Reference Angle = 45º
sin 135º = 2 tan 135º = -1
2
1
2
45º
-1
Target Goal:
#11
The students will be able to find
values of trigonometric
functions by using reference
angles.
• Sketch a -330º angle.
• Name the reference angle.
• Put the correct proportions for the
reference angle.
• Find the exact value for the
cos -330º and csc -330º.
Reference Angle = 30º
cos -330º = 3 csc (-330º) = 2
2
2
30º
-330º
3
1
Target Goal:
#12
The students will be able to find
values of trigonometric
functions by using reference
angles.
• Sketch a − 2π angle.
3
• Name the reference angle.
• Put the correct proportions for the
reference angle.
• Find the exact value for the
sec − 2π and cot − 2π .
3
3
Reference Angle = 60º=π
3




2
π
2
π



sec  −  =-2 cot  −  = 3
3

3

3
-1
− 3
60º
2
Target Goal:
#13
The students will be able to find
values of trigonometric
functions by using reference
angles.
• Sketch a 13π angle.
4
• Name the reference angle.
• Put the correct proportions for the
reference angle.
• Find the exact value for the
sec 13π and cot 13π .
4
4
Reference Angle = 45º=π
4
sec 13π = − 2
cot 13π = 1
4
4
-1
-1
45º
2
Target Goal:
The students will be able to
solve logarithmic equations
#14
Solve:
log 3x + log 4 = log 36
3
3
3
3
Do HW #12 Worksheet
(optional)
Solutions on Line
•It is your job to check
the HW solutions on
line.
•See me before school
in the math office with
any questions.
• See the board for the quiz
#6-#12 date.
• The quiz is individual with
the use of your foldable.
• 36 points