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1.
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Use the Law of Sines to
solve (if possible) for  . Round your answers to two decimal
places.
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2.
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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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3.
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Determine the area of a triangle having the
following measurements. Round your answer to two decimal places.
a. | 77.19 sq. units | b. | 64.32 sq. units | c. | 57.89 sq.
units | d. | 70.76 sq. units | e. | 51.46 sq. units |
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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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To determine the distance between two aircraft, a
tracking station continuously determines the distance to each aircraft and the angle between them
(see figure). Determine the distance a between the planes when   miles,   miles and   miles.
a. |  mi | b. | 
mi | c. |  mi | d. |  mi | e. |  mi |
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6.
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Find a unit vector in the direction of the given
vector.
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7.
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A force of F pounds is required to pull an
object weighing W pounds up a ramp inclined at  degrees from the
horizontal.
Find  if  pounds
and  .
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8.
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A traffic light weighing 16 pounds is suspended by
two cables (see figure). Find the tension in each cable if 
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9.
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Find the component form of vector
v.
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10.
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Find the magnitude and direction angle of  .
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11.
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final If  and  ,
and the vectors make angles of 40° and 100° and with the x-axis respectively, find
the component form of the sum of u and v. Round answers to two decimal
places.
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12.
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Three forces with magnitudes of 84 pounds, 83
pounds, and 135 pounds act on an object at angles 160°, 200°, and 280°, respectively,
with the positive x-axis. Find the magnitude and direction of the resultant force. Round
answers to two decimal places.
a. | 188.16 pounds; 224.81° | b. | 169.82 pounds; 224.81° | c. | 188.16 pounds; 44.81° | d. | 169.82 pounds; 44.81° | e. | 209.87 pounds; 256.33° |
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13.
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Find the dot product of u and
v.
a. | –27 | b. | –21 | c. | –25 | d. | –19 | e. | –23 |
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14.
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Find the dot product of u and
v.
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15.
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Find the dot product of u and
v.
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16.
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Find the angle  between the
vectors.
(Round the answer upto 1 decimal
place.)
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17.
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Find the angle  between the
vectors.
(Round the answer upto 2 decimal
places.)
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18.
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Find the projection of u onto
v.
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19.
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A tractor pulls a log 700 meters, and the tension
in the cable connecting the tractor and log is approximately 14,891 newtons. The direction of the
force is  above the horizontal. Approximate the work
done in pulling the log.
(Round the answer to two decimal places.)
a. | 8,538,595.16 N-m | b. | 8,538,635.16 N-m | c. | 8,538,655.16
N-m | d. | 8,538,615.16 N-m | e. | 8,538,675.16 N-m |
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20.
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A force of 60 pounds is exerted along a rope
attached to a crate at an angle of 30° above the horizontal. The crate is moved 42 feet.
How much work has been accomplished? Round answer to one decimal place.
a. | 2,351.2 foot-pounds | b. | 2,520.0 foot-pounds | c. | 2,909.8
foot-pounds | d. | 2,182.4
foot-pounds | e. | 2,630.5
foot-pounds |
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