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 Q and tan R.  a. | tan Q =  ; tan R = 0.75 | c. | tan Q =  ; tan R =  | b. | tan Q =  ; tan R = 0.75 | d. | tan Q = 0.75; tan R =  |
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2.
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Determine the measure of ÐDBC to the nearest
tenth of a degree.  a. | 27.5° | b. | 24.8° | c. | 65.2° | d. | 62.5° |
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3.
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Determine the tangent ratio for ÐK. 
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4.
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Determine the length of side s to the nearest tenth of a
millimetre.  a. | 18.4 mm | b. | 43.5 mm | c. | 8.6 mm | d. | 9.5
mm |
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5.
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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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6.
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An airplane is flying at an altitude of 7000 m. At a certain time, the angle
between the ground and a person’s line of sight to the airplane is 22°. About how far away is the person from a point on the ground vertically
below the airplane, to the nearest hundred metres?
a. | 17 300 m | b. | 7500 m | c. | 2800 m | d. | 18 700
m |
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7.
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The angle between one shorter side of a rectangle and a diagonal is 64°. One longer side of the rectangle is 9.2 cm. What is the width of the
rectangle, to the nearest tenth of a centimetre?
a. | 4.0 cm | b. | 18.9 cm | c. | 8.3 cm | d. | 4.5
cm |
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8.
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A surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the
base of a tower. The angle between the horizontal and the line of sight to the top of the tower was
21°. Determine the height of the tower to the nearest tenth of a
metre.
a. | 157.8 m | b. | 23.0 m | c. | 24.5 m | d. | 65.8
m |
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9.
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Determine sin G and cos G to the nearest hundredth.  a. | sin G = 0.99; cos G = 6.54 | c. | sin G = 1.01; cos G = 0.15
| b. | sin G = 0.15; cos G = 0.99 | d. | sin G = 0.99; cos G = 0.15 |
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10.
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A helicopter is hovering 200 m above a road. A car stopped on the side of the
road is 300 m from the helicopter. What is the angle of elevation of the helicopter measured from the
car, to the nearest degree?
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11.
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Determine the measure of ÐY to the nearest tenth
of a degree.  a. | 27.6° | b. | 62.4° | c. | 65.1° | d. | 24.9° |
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12.
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Determine the measure of ÐV to the nearest tenth
of a degree.  a. | 59.5° | b. | 36.1° | c. | 30.5° | d. | 53.9° |
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13.
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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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14.
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Determine the length of RS to the nearest tenth of a metre.  a. | 19.7 m | b. | 5.7 m | c. | 18.0 m | d. | 64.3
m |
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15.
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A wheelchair ramp is 7.0 m long. Its angle of inclination is 9°. Calculate the rise of the ramp to the nearest tenth of a
metre.
a. | 1.0 m | b. | 44.7 m | c. | 1.1 m | d. | 6.9
m |
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16.
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A tree broke 14 ft. above the ground. The top of the tree now touches the level
ground and the trunk is still partially attached to the stump. The angle of inclination of the tree
is 43°. To the nearest foot, determine the height of the tree before
it broke.
a. | 35 ft. | b. | 33 ft. | c. | 29 ft. | d. | 21
ft. |
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17.
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Solve this right triangle. Give the measures to the nearest tenth. 
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18.
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Solve this right triangle. Give the measures to the nearest tenth. 
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19.
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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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20.
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Determine the length of QR to the nearest metre.  a. | 85 m | b. | 170 m | c. | 127 m | d. | 118
m |
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Short Answer
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21.
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a) For ÐM in the triangle below, label the
hypotenuse and the opposite and adjacent sides. b) Determine tan M to the nearest
hundredth. 
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22.
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A tree is supported by a guy wire. The guy wire is anchored to the ground 7.0 m
from the base of the tree. The angle between the wire and the level ground is 60°. How far up
the tree does the wire reach, to the nearest tenth of a metre?
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23.
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A ladder is 7 m long. It leans against a house. The base of the ladder is 2 m
from the house. What is the angle of inclination of the ladder to the nearest tenth of a
degree?
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24.
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A 2.7-m cable is attached to a sign. The cable is anchored to the ground 1.8 m
from the base of the sign. What is the angle of inclination of the cable to the nearest tenth of a
degree?
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25.
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A tree is supported by a guy wire. The wire is anchored to the ground 7.0 m from
the base of the tree. The angle of inclination of the wire is 65°. Calculate the length of the
wire to the nearest tenth of a metre.
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Problem
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26.
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A rectangle measures 7.9 cm by 5.2 cm. Determine the measure, to the nearest
degree, of the acute angles formed by the intersection of the diagonals.
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27.
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The angle between one longer side of a rectangle and a diagonal is 37°. One
shorter side of the rectangle is 6.2 cm.
a) Sketch and label the rectangle.
b) What is the
length of the rectangle to the nearest tenth of a centimetre?
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28.
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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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29.
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Solve DLMN. Give the measures to the nearest tenth.
Explain your strategy. 
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30.
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The length of the body diagonal in this rectangular prism is 61 cm. The width of
the prism is 29 cm. The measure of ÐAFH is 23 °. Determine the height and the length of the rectangular prism to the
nearest centimetre. 
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