Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the reference angle for 140° in standard
position?
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2.
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What is the reference angle for 230° in standard
position?
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3.
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What are the three other angles in standard position that have a reference angle
of 81°?
A | 162°, 243°, 324° | C | 171°, 261°, 351° | B | 99°, 261°, 279° | D | 126°, 171°, 261° |
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4.
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What is the exact cosine of ÐA?  A | 1 | C |  | B | 9 | D |  |
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5.
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The point (–24, –70) is on the terminal arm of ÐA. Which is the set of exact primary trigonometric ratios for the
angle?
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6.
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The coordinates of a point P on the terminal arm of an angle are shown. What are
the exact trigonometric ratios for  ,  , and  ? 
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7.
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Marco is 950 m due east of the centre of the park. His friend Ray is 950 m due
south of the centre of the park. Which is the correct expression for the exact distance between the
two boys?
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8.
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Which strategy would be best to solve for x in the triangle
shown?  A | sine law | C | primary trigonometric ratios | B | cosine
law | D | none of the
above |
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9.
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Determine the measure of x, to the nearest tenth of a degree.  A | 20.0° | C | 70.0° | B | 50.5° | D | 109.5° |
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10.
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What is the length of x, to the nearest tenth of a metre?  A | 12.5 m | C | 41.2 m | B | 18.7 m | D | 32.8 m |
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Short Answer
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1.
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The hypotenuse of a right isosceles triangle is 5 cm long.
a) Write
an exact expression for the base and the height of the right triangle, using primary trigonometric
ratios.
b) Use your expressions to determine the exact area of the triangle.
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2.
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A drive belt wraps around three pulleys, A, B, and C, as shown.  What is the measure of  ?
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3.
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a) For the given trigonometric ratio, determine two other angles that
give the same value.
i) sin 45°
ii) tan 300°
iii) cos
120°
b) Explain how you determined the angles in part a).
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Problem
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1.
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An airplane is flying over the town of Colonsay, between two tracking stations.
The angle of elevation from Station 1 is 36° and from Station 2 is 48°. If the stations are
1675 m apart, what is the altitude of the plane, to the nearest tenth of a metre?
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2.
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Two ranger stations, A and B, are located in a pine forest and are 10 km apart.
A forest fire breaks out at point F and is spotted by both rangers. The angle formed at station A by
the line of sight to the fire and the line to station B is 63.2°. The angle at station B formed
by the line of sight to the fire and the line between the ranger stations is 57.9°.
a)
How far is station A from the fire, to the nearest tenth of a kilometre?
b) How far is
station B from the fire, to the nearest tenth of a kilometre?
c) Which ranger is closer to
the fire, and by how much?
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