Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine tan A and tan C.  a. | tan A = 1.25; tan C = 0.8 | c. | tan A = 0.8; tan C =
1.25 | b. | tan A = 0.8; tan C = 0.7809... | d. | tan A = 0.6247...; tan C =
1.25 |
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2.
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Determine the measure of ÐABD to the nearest
tenth of a degree.  a. | 65.1° | b. | 67.2° | c. | 22.8° | d. | 24.9° |
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3.
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A guy wire is attached to a tower at a point that is 10 m above the ground. The
wire is anchored 21 m from the base of the tower. What angle, to the nearest degree, does the guy
wire make with the ground?
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4.
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The height of the Telus Plaza South in Edmonton is about 134 m. Stacy is lying
on the ground near the building. The angle between the ground and her line of sight to the top of the
building is 75°. About how far is Stacy from the base of the
building, to the nearest metre?
a. | 139 m | b. | 500 m | c. | 129 m | d. | 36
m |
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5.
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A road has an angle of inclination of 16°.
Determine the increase in altitude of the road, to the nearest metre, for every 150 m of horizontal
distance.
a. | 523 m | b. | 144 m | c. | 43 m | d. | 41
m |
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6.
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From a point 18 ft. from the base of a flagpole, Seema used a clinometer to
sight the top of the flagpole. Seema held the clinometer 5 ft. 3 in. above the ground. The angle
between the horizontal and the line of sight was 52°. Determine the
height of the flagpole to the nearest foot.
a. | 28 ft. | b. | 34 ft. | c. | 19 ft. | d. | 23
ft. |
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7.
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A ladder is 13.0 m long. It leans against a wall. The base of the ladder is 3.7
m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a
degree?
a. | 73.5° | b. | 16.5° | c. | 74.1° | d. | 15.9° |
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8.
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A rope that anchors a hot air balloon to the ground is 136 m long. The balloon
is 72 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a
degree?
a. | 58.0° | b. | 62.1° | c. | 32.0° | d. | 27.9° |
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9.
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A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure
of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a
degree?
a. | 33.3° | b. | 61.3° | c. | 56.7° | d. | 28.7° |
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10.
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A balloon is flying at the end of a 170-m length of string, which is anchored to
the ground. The angle of inclination of the string is 50°. Calculate
the height of the balloon to the nearest metre.
a. | 130 m | b. | 143 m | c. | 109 m | d. | 222
m |
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11.
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A submarine ascends to the surface from the ocean floor (assume the submarine is
on level ground). The distance measured along the submarine’s path is 600 m. The angle of
inclination of the submarine’s path is 21°. Determine the
horizontal distance that the submarine travelled to the nearest metre.
a. | 230 m | b. | 560 m | c. | 643 m | d. | 215
m |
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12.
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Solve this right triangle. Give the measures to the nearest tenth. 
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13.
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Determine the length of this wheelchair ramp to the nearest hundredth of a
metre.  a. | 4.60 m | b. | 7.50 m | c. | 4.46 m | d. | 4.54
m |
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14.
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A water taxi leaves its dock, and travels 7 km due north to pick up medical
supplies. It then travels 15 km due east to drop off the supplies at a hospital. To the nearest
degree, what is the measure of the angle between the path it took due east and the path it will take
to return directly to its dock?
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15.
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A road rises 1 m for every 19 m measured along the road. To the nearest metre,
how far does a car travel horizontally when it travels 300 m along the road?
a. | 300 m | b. | 16 m | c. | 19 m | d. | 300 m |
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16.
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The front of a tent has the shape of an isosceles triangle with equal sides 163
cm long. The measure of the angle at the peak of the tent is 105 °.
Calculate the maximum headroom in the tent to the nearest centimetre.  a. | 129 cm | b. | 125 cm | c. | 99 cm | d. | 231
cm |
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17.
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Determine the perimeter of an equilateral triangle with height 11.9 cm. Give the
measure to the nearest tenth of a centimetre.
a. | 81.8 cm | b. | 41.2 cm | c. | 30.9 cm | d. | 71.4
cm |
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18.
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Calculate the measure of ÐGHJ to the nearest
tenth of a degree.  a. |  ° | b. | 29.3° | c. |  ° | d. | 68.0° |
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19.
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Calculate the measure of ÐABC to the nearest
tenth of a degree.  a. |  ° | b. | 102.5° | c. | 77.5° | d. |  ° |
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20.
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A tower is supported by two guy wires. The guy wires are anchored at the same
point on the ground,
8 m from the base of the tower. The angle of inclination of the longer guy
wire is 56° and the angle of inclination of the shorter guy wire is
32°. Determine the combined length of the guy wires to the nearest
metre.
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Short Answer
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21.
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Tan B = 1.3; determine the measure of ÐB to the
nearest tenth of a degree.
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22.
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Determine the length of side r to the nearest tenth of a
metre. 
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23.
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Determine the length of RT to the nearest tenth of a metre. 
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24.
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Determine the height of this isosceles triangle to the nearest tenth of a
centimetre. 
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25.
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Determine the length of WX to the nearest tenth of a centimetre. 
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Problem
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26.
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Determine the area of DABC to the nearest tenth of a
square unit. Determine its perimeter to the nearest tenth of a unit. 
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27.
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A boat was docked 30.0 m from the base of a cliff. A sailor used a clinometer to
sight the top of the cliff. The angle between the horizontal and the line of sight was 74°. The
sailor held the clinometer 1.5 m above the surface of the water. Determine the height of the cliff to
the nearest tenth of a metre.
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28.
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Guy wires are attached to buildings as shown. A student says the angles of
inclination of the wires are the same. Is the student correct? Justify your answer. 
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29.
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Solve DXYZ. Give the measures to the nearest tenth.
Explain your strategy. 
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30.
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A Girl Guide measured the angle of elevation of the top of a monument as 59 °. The height of the monument is 38.5 m. She then walked 31.0 m due west
from the point where she measured the angle of elevation. Determine the angle of elevation of the
monument from her new location to the nearest tenth of a degree. 
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