Transcript Thinking Mathematically by Robert Blitzer

February 7th
copyright2009merrydavidson
Happy Birthday to:
Madison Bynum 1/27
Nick Arnold 1/30
Dana Barber 2/6
Krystal Carmona 2/6
Applications of
Trigonometric
Functions
Section 4-8
Example 1:
A bridge is to be constructed across a small river from post A
to post B. A surveyor walks 100 feet due south of post A. She
sights on both posts from this location and finds that the angle
between the posts is 73. Find the distance across the river from
post A to post B.
x
Post B
Post A
x
tan 73 
100
100 ft.
73○
It follows that x = 327.
The distance across the river from post A to post B is 327 feet.
Word problem means word answer!
Bearings
• We use bearings to describe the direction
something is traveling or the direction in which we
see something.
A bearing measures the
acute angle that a path or
line of sight makes with a
fixed north/south line.
Reading Bearings
• Many directions are given using a
combination of two cardinal headings and
degree number
• North (N) and South (S) are always first
• Then the number of degrees
• Finally the East (E) or West (W) heading
• Example: N 53° W
Reading Bearings
N
40º
B
A
20º
W
O
75º
D
C
25º
S
Bearing to A:
N 70° E
Bearing to B:
N 40° W
Bearing to C:
S 15° W
Bearing to D:
S 25° E
E
Example 2
A boat leaves the entrance of a harbor and travels 40 miles on a
bearing of S64E. How many miles south and east did the has the
boat traveled?
S64E
40
miles
a
cos 64 
a
b
sin 64 
40
40 cos 64  a
b
17.5  a
40
40 sin 64  b
36  b
17.5 miles south, 36 miles east
Alternate Bearing Method
• Problems may just give you a single bearing
• 130 degrees
• This is always referenced from North
clockwise to the bearing (heading).
N
130
3) Draw a right triangle with right
angle at C, angle A = 34.2 degrees,
side “b” = 19.4 mm.
Solve the triangle
(solve
means
find
all
of
the
other
B
sides and angles).
C
34.2
19.4mm
A
B = 55.80, a = 13.2 mm, c = 23.5 mm
4) A safety regulation states that the
maximum angle of elevation for a rescue
ladder is 720. A fire department’s longest
ladder is 110 ft. What is the maximum
safe rescue height?
104.6 ft
5) At a point 200 feet from the base of a
building, the angle of elevation to the
bottom of a smokestack is 350, whereas
the angle of elevation to the to of the
smokestack is 530. Find the height “s” of
the smokestack alone.
125.4 ft.
6) A swimming pool is 20 meters long and
12 meters wide. The bottom of the pool is
slanted so that the water depth is 1.3
meters at the shallow end and 4 meters at
the deep end. Find the angle of
depression of the bottom of the pool.
top of water: 20m
7.70
1.3m
4m
angle of depression
7) Draw a diagram that represents
each bearing.
a)
b)
c)
d)
e)
bearing of 320
bearing of 300
N 420 E
S 310 E
N 520 W
Homework
Section 4-8; pg 359-361
Questions 16,18,20,22,30,36,37
Draw pictures, show all work for credit!