AP Pre-Calculus Law of Sines and Cosines Applications

AP Pre-Calculus Law of Sines and Cosines Applications

AP Pre-Calculus students will find exercises focused on the Law of Sines and Law of Cosines applications. This homework includes real-world problems involving triangles, bearings, and forces, designed to enhance understanding of trigonometric concepts. Topics covered include calculating distances, angles, and forces in various scenarios, making it ideal for students preparing for exams. The exercises encourage problem-solving skills and practical application of trigonometric principles.

Key Points

  • Includes application problems using the Law of Sines and Cosines for triangles.
  • Covers real-world scenarios like navigation and construction projects.
  • Features exercises on bearings and their calculations in trigonometry.
  • Designed for AP Pre-Calculus students to enhance problem-solving skills.
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  • Mayflowers
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AP
Pre-Calculus
Name
Lau
of
Stas
and
Lau
of
Corines
Aplications
Solve
the
following
application
exercises
utilizing
the
Law
of
Sines
and
/or
Law
of
Cosines.
Show
all
work
on
a
separate
piece
of
paper
and
keep
your
answers
with
your
work.
1.
A
triangular
piece
of
land
in
a
park
is
to
be
made
into
a
flower-bed.
Stakes
have been
driven
into
the
ground
at
the
vertices
of
a
triangle
which
we
call
B, E,
and
D.
The
gardener
can
only
locate
the
two
stakes
at
B
and
E.
BE
measures
6.2
meters,
and
the
gardener
recalls
that
the
angle
at
B
is
60° and
the
side
opposite
the
60°
is
to
be
5.5
meters
n
length.
Based
on
this
information
how
far
from
B
should
the
gardener
search
for
the
missing
stake?
2.
A
small
ship
travels
from
a
lighthouse
whose
light
only
shines
East
on
a
bearing
of
N 70°
E
a
distance
of
8
miles.
It
then
makes
a
turn
to
the
right
and
travels
for
Smiles
and
finds
itself
directly
in
the
beam
of
the
lighthouse’s
light.
How
far
from
the
lighthouse
is
the
ship?
3.
An
airline
route
from
San
Francisco
to
Honolulu
is
on
a
bearing
of
233°.
A
jet
flying
450
mph
flies
into
a
wind
blowing
39
mph
from
a
direction
of
114°.
Find
the
resulting
bearing
and
groundspeed
of
the
plane.
4.
A
bridge
is
to
be
built
across
a
lake
from
point
B
to
point
C.
The
bearing
from
B
to
Cis
S
41°
W.
From
point
A,
100
yards
from
B,
the
bearings
to
B
and
Care
S
74°
E
and
S
28°
E
respectively.
Find
the
distance
from
B
to
C.
5.
A
pilot
wishes
to
fly
on
a
course
of
70°
when
the
wind
is
blowing
30
mph
from
the
direction
of
145°.
If
he
plans
an
air
speed
of
125
mph,
what
wind
correction
angle
must
the
pilot
use?
6.
An
office
safe
was
lowered
from
an
office
building
by
two
cables
attached
to
buildings
on
opposite
sides
of
a
street.
At
one
time
the
cables
formed
angles
of
42°
and
76°respectively,
with
the
buildings.
Find
the
pull
on
each
of
the
cables
if
the
safe
weighed
1,250
pounds.
7.
A
plane
flies
650
mph
on
a
bearing
of
175.3°.
A
25
mph
wind,
from
a
direction
of
266.6°,
blows
against
the
plane.
Find
the
resulting
bearing
of
the
plane.
8.
A100
foot
vertical
tower
is
to
be
erected
on
the
side
of
a
hill
that
makes
an
8°
angle
with
the
horizontal.
Find
the
length
of
each
of
the
guide-wires
that
will
be
anchored
75
feet
uphill
and
downhill
from
the
base
of
the
tower.
9.
A
pilot
is
flying
at
168
mph
and
she
wants
her
flight
path
to
be
on
a
course
of
57°
40’.
A
wind
blowing
from
a
bearing
of
176°
28'35"
at
27.1
mph.
Find
the
bearing
the
pilot
should
fly
and
the
plane’s
groundspeed.
10.
Three
forces
of
54.2
pounds,
86.1
pounds,
and
110.4
pounds
act
at
angles
of
48°
15’,
123°
30’,
and
56°
15’
respectively,
with
the
horizontal.
Find
the
sum
of
their
horizontal
components
and
the
sum
of
their
vertical
components.
11.
A
mechanical
engineer
needs
our
help.
He
needs
to
model
the
motion
of
a
part
algebraically.
He
has
been
commissioned
to
build
a
machine
that
contained
a
link
like
pictured
in
the
illustrations.
One
end
of
the
link
is
affixed
to
a
slider
G.
As
the
circle
turns,
point
G
slides
back
and
forth
between
H
and
J,
never
touching
either.
Think
of
the
wheels
of
a
locomotive
to
illustrate
this
motion.
The
problem
he
needs
you
to
solve
is
how
to
mathematically
model
the
motion
of
G.
Kane
The
enhancad
link
SACD
reflected
over
the
center
fine
/ 2
End of Document
205
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FAQs of AP Pre-Calculus Law of Sines and Cosines Applications

What types of problems are included in the AP Pre-Calculus homework?
The homework includes a variety of application problems that utilize the Law of Sines and the Law of Cosines. Students will encounter scenarios such as calculating distances between points, determining angles in navigation, and analyzing forces acting on objects. Each problem is designed to reinforce the understanding of trigonometric principles in practical contexts.
How does the Law of Sines apply to real-world scenarios?
The Law of Sines is used to find unknown lengths and angles in non-right triangles, which is crucial in fields like architecture, engineering, and navigation. For example, when determining the distance between two points on a map, the Law of Sines can help calculate the necessary angles and distances based on known values. This application is essential for accurate measurements in various real-world situations.
What is the significance of bearings in trigonometry?
Bearings are used to describe direction in navigation and surveying, typically measured in degrees from North. Understanding how to calculate bearings is essential for accurately determining the position of objects or locations on a map. In the context of the homework, students will learn to apply trigonometric principles to solve problems involving bearings, enhancing their spatial reasoning and navigation skills.
What concepts are reinforced through the exercises in this homework?
The exercises reinforce key concepts such as the Law of Sines, the Law of Cosines, and their applications in solving triangles. Students will also practice calculating angles and distances in various contexts, which is vital for mastering trigonometry. Additionally, the problems encourage critical thinking and problem-solving skills, essential for success in AP Pre-Calculus and beyond.

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