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 200° in standard
position?
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2.
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What are the three other angles in standard position that have a reference angle
of 54°?
A | 99°, 144°, 234° | C | 144°, 234°, 324° | B | 108°, 162°, 216° | D | 126°, 234°, 306° |
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3.
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What is the exact sine of ÐA?  A | 1/ | C | 2/ | B | 1/3 | D | 1/2 |
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4.
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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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5.
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What is the exact value for  ?
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6.
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Which of the following triangles cannot be solved using the sine
law?
Diagrams not drawn to
scale.
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7.
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If  , c = 10.3 cm, and b = 10.5 cm, and DABC is acute, what is the measure of  , to the nearest tenth
of a degree? 
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8.
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Which strategy would be best to solve for x in the triangle
shown?  A | cosine law | C | sine law | B | primary trigonometric ratios | D | none of the
above |
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9.
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Solve the following triangle, rounding side lengths to the nearest tenth of a
unit and angle measures to the nearest degree.  Diagram not drawn to scale.
 , b =
19, a = 23.5
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10.
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While flying, a helicopter pilot spots a water tower that is 7.4 km to the
north. At the same time, he sees a monument that is 8.5 km to the south. The tower and the
monument are separated by a distance of 11.4 km along the flat ground. What is the angle made by the
water tower, helicopter, and monument? 
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Short Answer
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1.
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A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the
base of the rectangle.
a) Write an exact expression for the base and the height of the
rectangle.
b) Use your expressions to find the exact area of the rectangle.
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2.
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The point A(–3, –5) is on the terminal arm of an angle q. Determine exact expressions for the primary trigonometric ratios for the
angle.
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3.
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Diana is designing a triangular race course for a sailing regatta. The course is
triangular and has a 35° angle between two sides of 7 km and 6 km. What is the length of the
third side of the race course, to the nearest kilometre?
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Problem
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1.
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Consider ÐA such that cos A =  . a)
In which quadrant(s) is this angle? Explain. b) If the sine of the angle is negative, in
which quadrant is the angle? Explain. c) Sketch a diagram to represent the angle in
standard position, given that the condition in part b) is true. d) Find the coordinates of
a point on the terminal arm of the angle. e) Write exact expressions for the other two
primary trigonometric ratios for the angle.
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2.
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Sheryl is surveying a cliff to determine the elevation from the base of a canyon
to the top of the cliff. She lays out a line AB that is 225 m in length. She also sites a point C at
the base of the cliff. Point D is a point directly above point C, at the top of the cliff. She
measures  to be 43°,  to be 58°, and the angle of elevation from point A to
point D to be 29°. a) Draw a diagram to model this situation. b) Which side
will you calculate first and which tool will you use? c) Perform the calculation in part
b). d) Which tool can now be used to find the height of the cliff? e) Use this
tool to solve for the height of the cliff, to the nearest tenth of a metre.
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