Chapter 5: The
Trigonometric
Functions
Section 5-4: Applying
Trigonometric Functions
Finding the measures of the
sides of right triangles
• Trigonometric functions can be used to
solve problems involving right
triangles.
Example # 1
• If J= 50 degrees and j=12, find r.
•
G
r
•
12
50
R
g
J
12
o
sin 50 =
r
12
.76604 =
r
12
r=
.76604
r ≈ 15.7
Example #2
•
•
•
The chair lift at a ski resort rises at an angle of 20.75 degrees and
attains a vertical height of 1200 feet.
#1 How far does the chair lift travel up the side of the mountain?
# 2 A film crew in a helicopter records an overhead view of a
skier’s downhill run from where she gets off the chair lift at the
top to where she gets back on the
chair lift for her next run. If the
helicopter follows a level flight
path, what is the length of that
path?
1200
d
1200
.35429 =
d
1200
d=
.35429
d ≈ 3387 ft
(1200)2 + x 2 = (3387 )2
sin 20.75o =
d
#1
1200
20.75
#2
x 2 = 11471769 − 1440000
x 2 = 10031769
x ≈ 3167.3 ft
Example #3
•
•
•
•
•
•
•
•
•
•
A regular hexagon is inscribed in a circle with diameter 26,6 centimeters.
Find the apothem of the hexagon.
The apothem of a regular polygon is the measure of a line segment from
the center of the polygon to the midpoint of one of its sides.
First we know this is a hexagon and so the
angle OMN is 60 degrees. And we know
that the apothem bisects the angle so OMB
is 30 degrees. Thus angle BOM must be 60
degrees. Segment OM is a radius of the
circle and since the diameter is 26.6, we
M
know the radius is 13.3. Now using the
trigonometric functions, we can find a.
a
O
a
13.3
a
.86603 =
13.3
a ≈ 11.5cm
cos 30o =
N
Elevation and Depression
•
•
•
Surveyors use special instruments to find the measures of
angles of elevation and angles of depression.
An angle of elevation is the angle between a horizontal line
and the line of sight from an observer to an object at a higher
level.
An angle of depression is the angle between a horizontal
line and the line of sight from the observer to an object at a
lower level.
Example #4
•
An observer in the top of a lighthouse determines that the angles of
depression to two sailboats directly in line with the lighthouse are 3.5
degrees and 5.75 degrees. If the observer is 125 feet above sea level, find
the distance between the boats. We have two triangles.
Y
X
3.5
5.75
125
125
125
x
x = 2043.82
tan 3.5o =
5.75
3.5
125
y
y = 1241.43
tan 5.75o =
125 ft
•
So now we subtract 2043.82 - 1241.43= 802 feet
HW#35
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•
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Section 5-4
Pp. 302-304
#10-21 all, 25, 26, 28
32,33,34