Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which ratios are equivalent for all three side-angle pairs in acute
triangles?
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2.
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Determine the length of c to the nearest tenth of a
centimetre.
 a. | 23.0 cm | b. | 25.0 cm | c. | 24.0
cm | d. | 26.1 cm |
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3.
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Determine the measure of ÐR to the
nearest degree.
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4.
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Determine the measure of q to the nearest
degree.
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5.
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Determine the measure of q to the nearest
degree.
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6.
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In DXYZ, ÐX
= 51°, x = 7.0 cm, and ÐZ = 41°.
Determine the length of side y to the nearest tenth of a centimetre.
a. | 11.0 cm | b. | 10.0 cm | c. | 9.0
cm | d. | 8.0 cm |
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7.
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In DLMN, l = 27.0 cm, m = 31.4
cm, and ÐN = 82°.
Determine the measure of n
to the nearest tenth of a centimetre.
a. | 39.0 cm | b. | 38.5 cm | c. | 39.5
cm | d. | 38.0 cm |
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8.
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In DXYZ, x = 18 cm, y = 14 cm,
and z = 17 cm.
Determine the measure of ÐZ to the
nearest degree.
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9.
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How you would determine the indicated angle measure, if it is possible?  a. | the sine law | b. | not possible | c. | primary
trigonometric ratios | d. | the cosine law |
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10.
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How you would determine the indicated side length, if it is possible?  a. | the cosine law | b. | primary trigonometric
ratios | c. | not possible | d. | the sine law |
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11.
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A kayaker estimates the angle of elevation to the top of a cliff to be 20°.
He paddles closer to the cliff and the angle of elevation changes to 45°.
How you would
determine the distance to the cliff, if it is possible?
a. | the sine law | b. | primary trigonometric
ratios | c. | the cosine law | d. | not possible |
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12.
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A bush pilot delivers supplies to a remote camp
by flying 310 km in the direction N12°W. While at the camp, the pilot receives a radio message
to pick up a passenger at a village. The village is 70 km S61°W from the camp.
How
would you determine the distance from the village to the starting point? a. | primary trigonometric ratios | b. | the sine law | c. | the cosine
law | d. | not possible |
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13.
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How long, to the nearest inch, is the right rafter in the roof shown?
 a. | 34¢6¢¢ | b. | 33¢6¢¢ | c. | 33¢0¢¢ | d. | 34¢0¢¢ |
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14.
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A radar operator on a ship discovers a large
sunken vessel lying parallel to the ocean surface, 120 m directly below the ship. The length of the
vessel is a clue to which wreck has been found. The radar operator measures the angles of depression
to the front and back of the sunken vessel to be 55° and 46°. How long, to the nearest
tenth of a metre, is the sunken vessel?
a. | 203.7 m | b. | 201.8 m | c. | 199.9
m | d. | 198.0 m |
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15.
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In a parallelogram, two adjacent sides measure 20 cm and 27 cm.
The shorter
diagonal is 23 cm. Determine, to the nearest degree,
the measures of the larger angles in
the parallelogram.
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Short Answer
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16.
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Determine the measure of a to the nearest
degree.
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17.
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How would you determine the indicated angle measure, if it is possible?
Explain briefly. 
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18.
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A radar operator on a ship discovers a large sunken vessel lying parallel to the
ocean surface, 180 m directly below the ship. The length of the vessel is a clue to which wreck has
been found. The radar operator measures the angles of depression to the front and back of the sunken
vessel to be 52° and 67°. How long, to the nearest tenth of a metre, is the sunken
vessel?
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Problem
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19.
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In DTUV, ÐU
= 60°, u = 8.7 m, and v = 7.6 cm.
Solve the triangle. Round angles to the
nearest degree and sides
to the nearest tenth of a metre. Show your work.
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20.
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A parallelogram has sides that are 10 cm and 12 cm long.
One of the angles
in the parallelogram measures 55°.
Determine the length of the shorter diagonal to the
nearest tenth of a centimetre.
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21.
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A radio tower is supported by two wires on opposite sides. On the ground,
the ends of the wire are 46.5 m apart. One wire makes a 62° angle with the ground. The other
makes a 68° angle with the ground.
Draw a diagram of the situation. Then, determine the
height of the tower to the nearest tenth of a metre.
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