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1.
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Use the Law of Sines to
solve (if possible) the triangle. Round your answers to two decimal places.
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2.
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In the figure, and  are positive angles.
Write  as a function of  .
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3.
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A park ranger at point A observes a fire in
the direction  . Another ranger at point B, 5 miles due
east of A, sites the same fire at  . Determine the distance from point B to
the fire. Round answer to two decimal places.
a. | 2.18 miles | b. | 4.55 miles | c. | 2.51
miles | d. | 4.84 miles | e. | 4.20 miles |
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4.
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Use the law of Cosines to solve the given triangle.
Round your answer to two decimal places.
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5.
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Use the law of Cosines to solve the given triangle.
Round your answer to two decimal places.
  , b =
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6.
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Determine the angle  in the design
of the streetlight shown in the following figure.
 
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7.
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Given  ,  , and  , use the Law of Cosines to solve the triangle for the value of C. Round your
answer to two decimal places.
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8.
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Given  ,  , and  , use the Law of Cosines to solve the triangle for the value of c. Round your
answer to two decimal places.
a. | 16.29 | b. | 11.26 | c. | 15.57 | d. | 17.00 | e. | 14.13 |
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9.
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A vertical pole 29 feet tall stands on a hillside
that makes an angle of  with the horizontal. Determine the approximate
length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill
from the base of the pole. Round your answer to two decimal places.
a. | 82.88 feet | b. | 75.35 feet | c. | 99.45
feet | d. | 88.40 feet | e. |  feet |
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10.
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Select a linear combination of the standard unit
vectors i and j of given initial and terminal points of a vector.
Initial Point | Terminal Point | | | | |
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11.
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12.
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Find a unit vector in the direction of  .
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13.
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14.
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Given vectors  and  determine the quantity indicated below.
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15.
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A 725-pound trailer is sitting on an exit ramp
inclined at 36° on Highway 35. How much force is required to keep the trailer from rolling back
down the exit ramp? Round your answer to two decimal places.
a. | 566.49 pounds | b. | 546.44 pounds | c. | 586.54
pounds | d. | 506.34 pounds | e. | 426.14 pounds |
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16.
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Plot the complex number
and find its absolute value.
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17.
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Find the standard form
of the complex number. Then represent the complex number graphically.
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18.
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Find the trigonometric form of the complex number
shown below.
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19.
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Find the product  using
trigonometric forms. Leave the result in trigonometric form.
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20.
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Find the fifth roots of  Write the
roots in trigonometric form.
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