Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Calculate sin 16° to four decimal places. Predict another term that equals
sin 16°.
a. | –0.2756; sin 164° | b. | 0.2576; sin 164° | c. | 0.2756; –sin
16° | d. | none of the above |
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2.
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Which law could you use to determine the unknown side length in this
triangle?  a. | neither the sine law nor the cosine law | b. | the sine law
only | c. | the cosine law only | d. | the sine law and the cosine
law |
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3.
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Which law could you use to determine the unknown angle in this triangle?  a. | the sine law only | b. | neither the sine law nor the cosine
law | c. | the cosine law only | d. | the sine law and the cosine
law |
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4.
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Determine the unknown angle to the nearest degree. 
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5.
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Which set of measurements can produce two possible triangles?
a. | ÐA = 28°, a = 10.5 m, b =
15.0 m | b. | ÐA = 28°, a = 7.0 m, b =
15.0 m | c. | ÐA = 28°, a = 16.0 m, b =
15.0 m | d. | ÐA = 28°, a = 5.5 m, b =
15.0 m |
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6.
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Which set of measurements will produce one right triangle with b as the
hypotenuse?
a. | ÐA = 60°, a = 10.4 m, b =
12.0 m | b. | ÐA = 60°, a = 11.6 m, b =
12.0 m | c. | ÐA = 60°, a = 8.7 m, b =
12.0 m | d. | ÐA = 60°, a = 14.5 m, b =
12.0 m |
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7.
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Which set of measurements will produce just one triangle?
a. | ÐA = 25°, a = 9.4 m, b =
10.0 m | b. | ÐA = 40°, a = 9.4 m, b =
10.0 m | c. | ÐA = 125°, a = 9.4 m, b =
10.0 m | d. | ÐA = 70°, a = 9.4 m, b =
10.0 m |
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8.
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In DEFG, ÐG = 32°, f = 9.5 m, and g = 12.5 m.
Which
statement is true for this set of measurements?
a. | This is not a SSA situation. | b. | This is a SSA situation; no triangle is
possible. | c. | This is a SSA situation; only one triangle is possible. | d. | This is a SSA
situation; two triangles are possible. |
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9.
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In DKLM, LM = 16.0 cm and ÐL = 36°.
What is the height of the triangle from base
LK?
a. | 9.4 cm | b. | 9.2 cm | c. | 8.7 cm
| d. | 8.5 cm. |
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10.
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In DOPQ, PQ = 47 mm and ÐP = 47°.
What is the height of the triangle from base
PO?
a. | 32 mm | b. | 34 mm | c. | 35
mm | d. | 39 mm |
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11.
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In DCDE, DE = 9.0 cm and ÐD = 59°.
What is the height of the triangle from base
DC?
a. | 6.8 cm | b. | 7.1 cm | c. | 7.4 cm
| d. | 7.7 cm |
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12.
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In DNOP, OP = 175 mm and ÐO = 57°.
What is the height of the triangle from base
ON?
a. | 151 mm | b. | 147 mm | c. | 143
mm. | d. | 139 mm |
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13.
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Which would you use to determine the indicated angle measure?  a. | primary trigonometric ratios | b. | the sine law only | c. | the cosine law
only | d. | the sine law or the cosine law |
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14.
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Which would you use to determine the indicated angle measure?  a. | primary trigonometric ratios | b. | the sine law only | c. | the cosine law
only | d. | the sine law or the cosine law |
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15.
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Determine the indicated side length to the nearest tenth of a
centimetre.  a. | 9.0 cm | b. | 4.6 cm | c. | 7.0
cm | d. | cannot be determined |
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Short Answer
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16.
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Determine the unknown side length to the nearest tenth of a
centimetre. 
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17.
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In DMNO, ÐM = 33°, n = 6.2 cm, and o = 4.9 cm. Does this
involve the SSA situation? If so, how many triangles with the given measurements are
possible?
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18.
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Determine the indicated side length to the nearest tenth of a
centimetre. 
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Problem
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19.
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While golfing, Vikram hits a tee shot from point T toward a hole at
H. However, the ball veers 20° and lands at B. The scorecard says that H is
320 m from T. Vikram walks 200 m to his ball. Sketch a diagram of this situation. How far, to
the nearest metre, is his ball from the hole? Show your work.
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20.
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A canoeist leaves the dock and paddles toward a buoy 560 m away. After reaching
the buoy, she changes directions and paddles another 110 m. From the dock, the angle between the buoy
and the canoeist’s current position measures 10°. How far is the canoeist from the
dock? Give two possible answers. Show your work.
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21.
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An obtuse triangle has two known side lengths: 10 cm and 11 cm. The angle
opposite the shorter side measures 15°. Calculate the measure of ÐA, the obtuse angle in the triangle, to the nearest degree. Show
your work.
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