6. (5 pts.) A triangle has two sides with lengths 5 feet and 8
feet. If the two sides meet in an angle of 60°, what is the
exact length of the third side??
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TEST03/MAC1114
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7. (5 pts.)
If the polar coordinates of a point are given by
(r,
θ
) = (7.5,110°), find the rectangular coordinates for the
point. In doing this, make clear which values are exact and
which are approximations.
8. (5 pts.)
If the rectangular coordinates of a point are
given by (x,y) = (2,2
√
3), obtain polar coordinates for the
point.
9. (5 pts.)
Suppose that the letters x and y represent
rectangular coordinates. Write the following rectangular
equation in terms of polar coordinates (r,
θ
).
y
2
= 2x
10. (5 pts.)
Suppose that the letters r and
θ
represent polar
coordinates. Write the following polar equation in terms of
rectangular coordinates (x,y). Can you identify the object??
r = 6 sin(
θ
)  8 cos(
θ
)
11. (5 pts.)
Plot the following polar points below. Label
carefully: A = (2,45°), B = (2,45°), C = (2,30°), D = (2,30°)
y
x
TEST03/MAC1114
Page 4 of 4
12. (10 pts.) To measure the height of the top of a distant
object , 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 50°. The second sighting,
which is most distant from the object, results in an angle of
elevation of 35°. 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. You may assume the object is on a level plane
with the base of the transit.]
13. (10 pts.) Use the Law of Sines to solve the triangle with
α
= 110°,
γ
= 30°, and c = 3. You may assume that the standard
labelling scheme is used.
14. (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 = 7,
α
= 70°
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 Spring '08
 Storfer
 Trigonometry, triangle, Polar coordinate system, α

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