If x denotes the length of the third side, then from the Law
of Cosines, we have x
2
=8
2
+5
2
 2(8)(5)(cos(30°)=89403
1/2
.
Thus,x=(89403
1/2
)
1/2
, exactly.
Note that x
≈
4.44 feet.
11. (10 pts.) Use the Law of Sines to solve the triangle with
α
= 110°,
γ
=3
0°
,a
n
dc=6
. Y
o
um
a
y assume that the standard
labelling scheme is used.
The missing pieces are
β
=4
0°, a = 12sin(110°)
≈
11.28, and
b = 12sin(40°)
≈
7.71.
12. (5 pts.) Determine whether one, two, or no triangles result
from the following data.
You do not have to solve the triangles
that might result.
You may assume that the standard labelling
scheme is used.
a=3
,b=6
,
α
=3
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13. (10 pts.)
To measure the height of the top of a distant
object on a level plane, a surveyor takes two sightings of the
top of the object 1000 feet apart. The first sighting, which is
nearest the object, results in an angle of elevation of 60°.
The
second sighting, which is most distant from the object, results
in an angle of elevation of 30°.
If the transit used to make the
sightings is 5 feet tall, what is the height of the object.
[Hint: Make a diagram of the situation.
The distance from the
base of the object is unknown. ]
Let h denote the height of the object, x the length of the
side opposite the 60° sighting, and d the length of the side
adjacent to the 60° angle. The sides of length d and x meet in a
right angle.
Then we haveh=x+5
,a
n
dt
h
e system of equations
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 Spring '08
 Storfer
 Pythagorean Theorem, Sin, pts, triangle

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