A surveyor is standing 115 ft from the base of the
Washington Monument. The surveyor measures the angle of
elevation to the top of the monument as 78.3 degrees.
What is the height of the Washington Monument?
Photo credit:
Retrieved address
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efurl=http://www
.visitingdc.
com/memorial
/washington
-monumentaddress
Draw a diagram. What are you looking for? What sides are of
interest ? What trigonometric function can you use?
h
o
78.3
115 ft
a
We want to find the opposite side and we know the
adjacent side. Therefore we can use the tangent
function.
Tan
78.3°
=
o
a
So, o =( a ) ( tan 78.3 degrees) =
(115 ft) (4.82882) = 555 ft
Answer: The Washington Monument is 555 ft tall.
Skateboard problem
A skateboard ramp has an angle of elevation of
18.4 degrees. The vertical side is 4 ft high.
What is the length of the skateboard ramp?
First draw a diagram.
Diagram
o
h
4 ft
a
18.4
degrees
What sides interest us? What trigonometric
function can we use?
We know the length of the opposite side and we
want to find the length of the hypotenuse. So we
can use the sin function
Sin 18.4
°=
a
h
a
4
ft
h=
=
sin18.4° .3156
= 12.7 ft
The length of the ramp is 12.7 ft
Homework problem:
# 64 p 310
A 6 ft person walks from the base
of a tower directly toward the tip
of the shadow cast by the tower.
When the person is 132 ft from the
tower and 3 ft from the tip of the
shadow, the person’s shadow
starts to appear beyond the
tower’s shadow. What is the height
of the tower?
a) Draw a
DIAGRAM
Photo credit:”moshilove photostream”
A
Diagram: What
are the
sides that interest us?
h
o
E
6 ft
B
a
132 ft
D
q
3 ft C
b) Use a trigonometric function to
write an equation involving the
unknown quantity?
In triangle EDC
Tan
q
=
o
a
=
6
3
=2
In triangle ABC
tan
q
=
o
(132 + 3)
In triangle EDC, tan
o
= 2,
(132 + 3)
q
= 2, so
so o = 2 (135 ft) = 270 ft
The height of the tower is 270 ft.
Note: The height of the Eiffel Tower is 1,050 ft 0r 520 m.
Find the height of the tower without
using a trigonometric function.
A
By what postulate are triangle ABC
and triangle EDC similar? What do you
you conclude about their sides?
E
B
D
C
Angle B and D are right angles, so they are
congruent and angle C
@
angle C (reflexive
property of congruence); so the triangles ABC and
EDC are similar by the AA Postulate.
Therefore, the corresponding sides of the triangles
are proportional.
o
6
=
(132 +3)
3
, so
o =(6)(135 ft)
3
= 270 ft
Homework problem: # 66, p. 310
A biologist wants to know the width w of a river
so in order to properly set instruments for
studying the pollutants in the water. From point
A, the biologist walks downstream 100 ft and
sights to point C. From this sighting, it is
determined that angle theta equals 54 degrees.
How wide is the river?
Diagram
C
w
river
q = 54°
A
100 ft
tan 54 degrees = w/ 100ft
so w = (tan 54 degrees )(100)
= ( 1. 376)(100)
= 137.6 ft
The river is 137.6 ft wide.
Homework Problem:
# 67 p. 310
Photo credit: kawwsu19’s photostream
One end of a steel cable zip-line is attached to a
platform on top of a 150 ft pole. The other end of
the zip-line is attached to the top of a 5-ft stake.
The angle of elevation of the platform is 23
degrees.
a) How long is the zip-line?
b )How far is the stake from the pole?
c) Contestants take an avarege of 6 seconds to
reach the ground from the top of the zip-line. At
what rate are contestants moving down the line?
At what rate are they dropping vertically?