Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Given  ,  , and  , use the Law of Sines to solve the triangle (if possible) for the value of b. If
two solutions exist, find both. Round answer to two decimal places.
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2.
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Determine a value for b such that a triangle
with  and  has no solution. Round your
answer to the nearest hundredth.
a. | 11.69 | b. | 2.36 | c. | 2.95 | d. | 5.90 | e. | 31.83 |
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3.
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Determine the area of a triangle having the
following measurements. Round your answer to two decimal places.
a. | 23.84 sq. units | b. | 28.61 sq. units | c. | 21.46 sq.
units | d. | 19.07 sq. units | e. | 26.22 sq. units |
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4.
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Given  ,  , and  , use the Law of Cosines to solve the triangle for the value of B. Round answer to
two decimal places.
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5.
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In the figure below,  ,  , and  . Use this information to solve the
parallelogram for c. The diagonals of the parallelogram are represented by c and
d. Round answer to two decimal places.
a. | 5.52 | b. | 12.15 | c. | 10.49 | d. | 9.25 | e. |  |
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6.
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In the figure below,  ,  , and  . Use this information to solve the
parallelogram for b. The diagonals of the parallelogram are represented by c and
d. Round answer to two decimal places.
a. | 12.77 | b. | 6.03 | c. | 11.08 | d. | 9.82 | e. | 9.40 |
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7.
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Find the component form of vector v with
initial point  and terminal point  .
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8.
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Find a unit vector in the direction of  .
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9.
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Find the magnitude and direction angle of  . Round direction angle to nearest degree.
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10.
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Find the component form of v if  and the angle it makes with the x-axis is 150°.
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11.
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Three forces with magnitudes of 95 pounds, 75
pounds, and 146 pounds act on an object at angles 100°, 200°, and 300°, respectively,
with the positive x-axis. Find the magnitude and direction of the resultant force. Round
answers to two decimal places.
a. | 41.84 pounds; 256.57° | b. | 41.84 pounds; 76.57° | c. | 60.18 pounds; 256.57° | d. | 60.18 pounds; 76.57° | e. | 81.89 pounds; 288.09° |
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12.
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Given vectors  and  determine the quantity indicated below.
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13.
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A force of 45 pounds is exerted along a rope
attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet.
How much work has been accomplished? Round answer to one decimal place.
a. | 1,035.0 foot-pounds | b. | 896.3 foot-pounds | c. | 1,195.1
foot-pounds | d. | 965.7
foot-pounds | e. | 1,080.4
foot-pounds |
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14.
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Find the trigonometric form of the complex number
represented graphically.
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15.
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Find the trigonometric form of  .
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16.
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Perform the operation shown below and leave the
result in trigonometric form.
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17.
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Find the product  using
trigonometric forms. Leave the result in trigonometric form.
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18.
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Use DeMoivre's Theorem to find the indicated
power of the complex number. Write the result in standard form.
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19.
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Use DeMoivre's Theorem to find the indicated
power of the following complex number.
a. |  | b. | –4,096 | c. | 2048 | d. | 4,096 | e. |  |
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20.
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Find the fourth roots of 
Write the roots in trigonometric form.
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