Objective
Green
Yellow
Red
6.1 Sketch an angle in standard position, given the measure of the angle.
6.2 Determine the reference angle for an angle in standard position.
6.3 Explain, using examples, how to determine the angles from 0° to 360° that
have the same reference angle as a given angle.
6.4 Illustrate, using examples, that any angle from 90° to 360° is the reflection in
the x-axis and/or the y-axis of its reference angle.
6.5 Determine the quadrant in which a given angle in standard position terminates.
6.6 Draw an angle in standard position given any point P(x, y) on the terminal arm
of the angle.
6.7 Illustrate that the points P(x, y), P(−x, y), P(−x, −y) and P(x, −y) are points on
the terminal sides of angles in standard position that have the same reference angle.
6.8 Determine, using the Pythagorean theorem or the distance formula, the distance
from the origin to a point P (x, y) on the terminal arm of an angle.
6.9 Determine the value of sin θ, cos θ or tan θ, given any point P (x, y) on the
terminal arm of angle θ.
6.10 Determine, without technology, the value of sin θ, cos θ or tan θ, given any
point P (x, y) on the terminal arm of angle θ, where θ = 0º, 90º, 180º, 270º or 360º.
6.11 Determine the sign of a given trigonometric ratio for a given angle, without
the use of technology, and explain.
6.12 Solve, for all values of θ, an equation of the form sin θ = a or cos θ = a, where
−1 ≤ a ≤ 1, and an equation of the form tan θ = a, where a is a real number.
6.13 Determine the exact value of the sine, cosine or tangent of a given angle with
a reference angle of 30º, 45º or 60º.
6.14 Describe patterns in and among the values of the sine, cosine and tangent
ratios for angles from 0° to 360°.
6.15 Sketch a diagram to represent a problem.
6.16 Solve a contextual problem, using trigonometric ratios.
6.17 Sketch a diagram to represent a problem that involves a triangle without a
right angle.
6.18 Solve, using primary trigonometric ratios, a triangle that is not a right triangle.
6.19 Explain the steps in a given proof of the sine law or cosine law.
6.20 Sketch a diagram and solve a problem, using the sine law.
6.21 Sketch a diagram and solve a problem, using the cosine law.
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 1
Math 20-1 Unit 6: Trigonometry Practice Booklet
Math 10C: Trigonometry Review
1) Determine the missing measures in each right triangle. Round side measures to one decimal place and angle
measures to the nearest degree.
2) At a point 28 m from a building, the angle of elevation to the top of the building is 65°. The observer’s eyes are
1.5 m above the ground. How tall is the building?
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 2
3) Two office towers are 30 m apart. From the top of the shorter tower, the angle of elevation to the top of the
other tower, which is 250 m high, is 70°.
a) How much taller is the taller tower?
b) Determine the height of the shorter tower.
c) Determine the angle of depression, to the nearest degree, to the base of the taller tower from the top of the
shorter tower.
4) Olivia looks out the window of her apartment building and sees a Corvette down the street at an angle of
depression of 18°. A little farther down the street, she sees a police car at an angle of depression of 15°. Her
apartment window is 35 m above street level. How far apart are the Corvette and the police car?
5. Two trees are 62 m apart. From a point on the ground halfway between the trees, the angle of elevation to the
top of one tree is 35 and the angle of elevation to the top of the other tree is 60 .
a) How far is the point on the ground from the base of the taller tree?
b) What is the height of the taller tree to the nearest metre?
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 3
6. Lovett Lookout is in Northern Alberta and has a height of 30 m. From the top of the lookout, a ranger sees two
fires. One is at an angle of depression of 7 and the other has an angle of depression of 3. The fires and the tower
are in a straight line. Find the distance between the fires, to the nearest metre, if they are
a) on the same side of the tower
b) on the opposite sides of the tower
6.1 Angles in Standard Position in Quadrant I
1. State whether each diagram represents an angle in standard position. Explain your thinking.
a)
b)
c)
d)
2. Point 𝑃(5, 8) is on the terminal arm of an angle 𝜃 in standard position.
a) Sketch the angle.
b) Determine the distance from the origin to 𝑃.
c) Write the primary trigonometric ratios of 𝜃.
d) What is the measure of 𝜃 to the nearest degree?
Math 20-1 Unit 6: Trigonometry Practice Booklet
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3. a) Use this diagram to determine the exact primary trigonometric ratios of 60°.
b) Use the diagram in part a to determine the exact primary trigonometric ratios of 30°.
4. For each angle below, determine the exact coordinates of a point on the terminal arm of the angle in standard
position. The diagram above may be useful.
a) 30°
b) 45°
c) 60°
5. A support cable is anchored 15 m from the base of a pole and is attached to the pole 10 m above the ground.
a) Determine the length of the cable to the nearest tenth of a metre.
b) To the nearest degree, what angle does the cable make with the ground?
6. Point 𝑃(𝑥, 𝑦) is on the terminal arm of each angle below in standard position. The distance r between P and the
origin is given. To the nearest tenth, determine the coordinates of P.
a) 20°, 𝑟 = 10
b) 80°, 𝑟 = 5
Math 20-1 Unit 6: Trigonometry Practice Booklet
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7. a) Determine the distance of each point from the origin.
i) 𝐴(4, 6)
ii) 𝐵(7, 3)
b) Each point is part a is on the terminal arm of an angle 𝜃 in standard position. For each angle, determine cos 𝜃,
sin 𝜃, tan 𝜃, and the measure of 𝜃 to the nearest degree.
i) 𝐴(4, 6)
ii) 𝐵(7, 3)
8. Each angle 𝜃 is in standard position in Quadrant I.
5
a) 𝑐𝑜𝑠𝜃 = 13, what are sin 𝜃 and tan 𝜃
c) tan 𝜃 =
3
√7
b) sin 𝜃 =
2
, what are tan 𝜃 and cos 𝜃?
√5
, what are sin 𝜃 and cos 𝜃?
9. A fire spotter sees smoke rising from a point that lies in a direction 𝐸80°𝑁. He estimates that the distance from
his location is about 20 km. The firefighters have to travel east then north to get to the fire. To the nearest
kilometre, how far should the firefighters travel in each direction?
Math 20-1 Unit 6: Trigonometry Practice Booklet
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6.2 Angles in Standard Position in All Quadrants
1. Sketch each angle in standard position.
a) 75°
b) 140°
c) 200°
2. a) Determine the reference angle for each angle in standard position.
i) 34°
ii) 98°
iii) 241°
d) 340°
iv) 290°
b) For each angle in part a, determine the others within the domain 0° ≤ 𝜃 ≤ 360° that have the same reference
angle.
i) 34°
ii) 98°
iii) 241°
iv) 290°
3. Determine the quadrant in which the terminal arm of each angle in standard position lies.
a) 280°
b) 88°
c) 191°
d) 103°
4. Each angle 𝜃 is in standard position. State the quadrants in which the terminal arm of the angle could lie.
2
1
a) 𝑐𝑜𝑠𝜃 = − 3
b) 𝑡𝑎𝑛𝜃 = −4
c) 𝑠𝑖𝑛𝜃 = 2
d) 𝑡𝑎𝑛𝜃 = 0.25
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 7
5. Point 𝑃(−3, 4) is a terminal point of an angle 𝜃 in standard position.
a) Sketch the angle.
b) What is the distance from the origin to P?
c) Write the primary trigonometric ratios of 𝜃.
d) To the nearest degree, what is 𝜃?
6. Each point below lies on the terminal arm of an angle 𝜃 in standard position. Determine:
i) Cos 𝜃
ii) Sin 𝜃
iii) Tan 𝜃
iv) the value of 𝜃 to the nearest degree
a) 𝐴(−3, −4)
b) 𝐵(−6, 0)
c) 𝐶(0, 2)
7. A hiker sketches a map of her destination, D, from her starting point, O. The hiker can travel only west, then
north. To the nearest kilometre, how far must she hike to get to her destination?
Math 20-1 Unit 6: Trigonometry Practice Booklet
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8. The location of the terminal arm of an angle ∝ and a trigonometric ratio of its reference angle 𝜃 are given.
1
a) The terminal arm lies in Quadrant III, 𝑡𝑎𝑛𝜃 = ; what is tan ∝?
4
b) The terminal arm lies in Quadrant II, 𝑡𝑎𝑛𝜃 =
−3
7
; what is 𝑠𝑖𝑛 ∝?
9. What values of 𝜃 satisfy each equation for 0° ≤ 𝜃 ≤ 360°?
a) 𝑡𝑎𝑛𝜃 = 1
b) 𝑡𝑎𝑛𝜃 = 0
d) 𝑠𝑖𝑛𝜃 = 0
e) cos 𝜃 = 1
c) sin 𝜃 = 1
f) 𝑐𝑜𝑠𝜃 = 0
10. To the nearest degree, which values of 𝜃 satisfy each equation for 0° ≤ 𝜃 ≤ 360°?
1
a) tan 𝜃 = 2
b) 𝑐𝑜𝑠𝜃 = 0.6
11. Which statements are correct?
i) 𝑐𝑜𝑠60° + 𝑠𝑖𝑛30° = 1
iii) 𝑐𝑜𝑠45° + 𝑠𝑖𝑛45° = √2
a) Only i and ii
b) Only iii and iv
c) No statements
Math 20-1 Unit 6: Trigonometry Practice Booklet
ii) 𝑠𝑖𝑛60° + 𝑐𝑜𝑠30° = √3
𝑐𝑜𝑠45°
iv) 𝑠𝑖𝑛45° = 1
Page 9
d) All statements
1
12. Angle 𝜃 is in standard position and its terminal arm lies in Quadrant IV. The cosine of its reference angle is 8.
Determine the exact values of sin 𝜃, cos 𝜃 and tan 𝜃.
3
13. Angle 𝜃 is in standard position, with 𝑡𝑎𝑛𝜃 = − 2. Which statement could be correct?
A. 𝑠𝑖𝑛𝜃 =
3
√13
B. cos 𝜃 = −
C. 𝑠𝑖𝑛𝜃 = −
D. cos 𝜃 =
3
√13
2
√13
3
√13
6.3 Sine Law
1. For each triangle, use the Sine Law to determine the length of AC.
a)
b)
2. For each triangle, use the Sine Law to determine the measure of < 𝐸.
a)
b)
Math 20-1 Unit 6: Trigonometry Practice Booklet
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3. For each triangle, determine the length of MN to the nearest tenth of a centimetre.
a)
b)
4. For each triangle below, can you use the Sine Law to determine the indicated measure? Justify your answer.
a)
b)
c)
d)
5. A surveyor constructed this scale drawing of a triangular lot.
a) Determine the unknown side lengths.
b) Determine the total length of fencing needed to enclose the lot. Give the answers to the nearest
centimetre.
Math 20-1 Unit 6: Trigonometry Practice Booklet
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6. Solve ∆𝑃𝑄𝑅 by drawing a perpendicular from P to QR, then use primary trigonometric ratios in each right
triangle formed.
Give the angle measure to the nearest degree and the side lengths to the nearest tenth of a centimetre.
7. A sailor made this sketch on her navigation chart. How much closer is the ship at S to lighthouse A than to
lighthouse B? Record your answer to the nearest tenth of a km.
8. Two ships are 1600 m apart. Each ship detects a wreck on the ocean floor. The wreck is vertically below the line
through the ships. From the ships, the angles of depression to the wrecks are 40° and 28°.
a) To the nearest metre, how far is the wreck from each ship?
b) To the nearest metre, what is the depth of the wreck?
Math 20-1 Unit 6: Trigonometry Practice Booklet
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9. A hiker plans a trip in two sections. Her destination is 15 km away on a bearing of 𝑁70°𝐸 from her starting
position. The first leg of the trip is on a bearing of 𝑁10°𝐸. The second leg of the trip is 14 km. How long is the
first leg? Give answers to the nearest tenth of a kilometre.
10. Two angles in a triangle measure 60° and 45°. The longest side is 10 cm longer than the shortest side.
Determine the perimeter of the triangle to the nearest tenth of a centimetre.
**Challenger
6.4 Cosine Law
1. Which strategy would you use to determine the indicated measure in each triangle?
 A primary trigonometric ratio
 The cosine law
 The sine law
Then determine each measure. Give the angles to the nearest degree and the side lengths to the nearest
tenth.
a)
b)
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 13
c)
d)
2. Determine the indicated measure in each triangle. Give the angles to the nearest degree and the side lengths to
the nearest tenth of a unit.
a)
b)
c)
Math 20-1 Unit 6: Trigonometry Practice Booklet
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3. Solve the following triangles. Give the side lengths to the nearest tenth of a unit and the angle measures to the
nearest degree.
a)
b)
4. In ∆𝐴𝐵𝐶, 𝐵𝐶 = 2𝐴𝐵, < 𝐵 = 120°, 𝑎𝑛𝑑 𝐴𝐶 = 14𝑐𝑚; determine the exact lengths of AB and BC.
5. Three circles have radii 3 cm, 4cm, and 5 cm. Each circle just touches the other 2 circles externally. To the
nearest tenth of a square centimetre, determine the area of the triangle formed by the center of the circles.
***Challenger
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 15
6. Here is a sketch of the route taken by an orienteering group on a one-day trek.
a) To the nearest tenth of a kilometre, what is the straight line distance from the start to the end?
b) To the nearest degree, what is the bearing of the endpoint from the start point?
7. The lengths of the sides of a parallelogram are 9 cm and 10 cm. The shorter diagonal is 12 cm long. To the
nearest tenth of a centimetre, what is the length of the longer diagonal?
Practice Test
1. Which of the following pairs of angles, in standard position, have the same reference angle?
a) 62° and 152°
b) 212° and 328°
c) 149° and 319°
d) 71° and 19°
2. The point (𝑥, 𝑦) is on th terminal arm of an angle 𝜃° in standard position. Which of the following statements are
true?
a) The point (𝑦, 𝑥) is on the terminal arm of angle 𝜃°.
b) The point (𝑥, −𝑦) is on the terminal arm of angle (180 − 𝜃)°.
c) The point (−𝑥, −𝑦) is on the terminal arm of angle (180 + 𝜃)°.
d) The point (−𝑥, 𝑦) is on the terminal arm of angle (360 − 𝜃)°.
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 16
3. In which quadrant is the sine ratio of an angle negative and the tangent ratio of the angle also negative?
a) IV
b) III
c) II
d) I
4. The terminal arm of angle 𝜃 in standard position passes through the point (8, −6). The exact value of sine is
a) 0.6
b) −0.6
c) 0.8
d) −0.8
5. Which of the following statements is true?
a) 𝑐𝑜𝑠 165° = 𝑐𝑜𝑠15°
b) sin 287° = −𝑠𝑖𝑛17°
c) tan 156° = −𝑡𝑎𝑛24°
d) sin 200° = 𝑠𝑖𝑛20°
6. Determine the exact value of cos 210°
√3
2
√3
2
1
a) −
b)
c) − 2
1
d) 2
4
7. Angle A terminates in the fourth quadrant with 𝑐𝑜𝑠𝐴 = . The exact value of tan 𝐴 is
5
4
a) 3
3
b) 4
4
c) − 3
3
d) − 4
8. The largest solution to the equation 𝑡𝑎𝑛𝜃 + 1 = 0, 0° ≤ 𝜃 ≤ 360°, is 𝜃 = 𝑥°.
a) 45°
b) 135°
c) 225°
d) 315°
9. The diagram shows an initial arm of length 1 unit being rotated counter-clockwise about the origin to form a
circle of radius 1. Two points on the circumference of the circle are A(−
counter-clockwise from A to B, the measure of angle AOB is
a) 75°
b) 105°
c) 165°
d) 195°
Math 20-1 Unit 6: Trigonometry Practice Booklet
√3 1
, )
2 2
√2
and B( 2 , −
√2
).
2
Rotating
Page 17
10. Solve: 𝑠𝑖𝑛𝐴 = −0.8290, 0° ≤ 𝐴 ≤ 360°
a) 56°
b) 56°, 124°
c) 124°, 236°
d) 236°, 304°
11. An oil company drilling off shore has pipelines from platform Alpha and platform Beta to the same shore
station Delta. Platform Alpha is 180 km on a bearing of 50° from Delta and platform Beta is 250 km on a bearing
of 125° from Delta. Calculate the distance between platform Alpha and platform Beta to the nearest km.
Use the following information to answer the next question
The first hole at a golf course is 210 yards long in a direct line from the tee to the first hole. Andrew Duffer hit his
first shot at an angle of 15° off the direct line to the hole. The angle between his first shot and his second shot was
105°. He second shot landed in the hole!!
12. The length of his second shot, to the nearest yard, was
a) 30
b) 56
c) 105
d) 188
13. Triangle ABC is drawn with AB=3.6 cm, BC=4.2 cm and angle BCA=28°. The measure of angle ABC is
a) 33°
b) 119°
c) 33° or 147°
d) 5° or 119°
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 18
14. Triangle LMN is obtuse angled at M and < 𝑀𝐿𝑁 = 40°. Sin LNM is equal to
a)
b)
c)
d)
𝐿𝑀𝑠𝑖𝑛40°
𝑀𝑁
𝐿𝑀
𝑀𝑁𝑠𝑖𝑛40°
𝑀𝑁
𝐿𝑀𝑠𝑖𝑛40°
𝑀𝑁𝑠𝑛40°
𝐿𝑀
Use the following diagram to answer the next two questions.
15. The length of QS, to the nearest tenth of a centimetre, is _____.
16. The measure of angle QSR, to the nearest degree, is _____.
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 19
Use the following information to answer the next question
A student has been given the following problem to solve.
“A pilot leaves an airport flying on a bearing of 165°. He changes direction and flies for 80 km on a
bearing of 205°. He changes direction again and flies back to the airport. How far is he from the airport
when he makes the second change in direction.”
17. The most appropriate method for solving this problem is
a) SOH CAH TOA
b) the Sine Law
c) the Cosine Law
d) the problem cannot be solved without further information.
Use the following information to answer the next question
On June 30, 1956, the world’s largest free standing totem pole
was erected in Beacon Hill Park in Victoria. Recently, a surveyor
took measurements to verify the height, h, of the totem pole.
In the diagram, triangle ABC lies in a vertical plan and triangle BCD
lies in a horizontal plane.
18. The height of the totem pole, to the nearest metre, is ____.
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 20
19. Mr. Post’s two metre high fence has almost been blown down by the wind. As a temporary measure, he wants
to tie a rope from the top of the fence to a peg one metre from the base of the fence.
The fence has moved so that it is leaning 25° to the vertical as shown. Determine, to the nearest tenth of a metre,
the minimum length of rope required if he allows 50 cm for knots.
a) 1.7 𝑚
b) 2.3 𝑚
c) 2.6 𝑚
d) 3.1 𝑚
20. At 5 pm, the distance between the tip of the minute hand on a clock and the tip of the hour hand is 17.4 cm. If
the minute hand is 10 cm long, the length of the hour hand, to the nearest tenth of a centimetre, is _______.
Answer Key:
Math 10C Review:
1.a) 13.3 b) 10.7 c) 52° d) 23.6
2. 62 m
4. 23 m
5. a) 31m
b) 54 m
6. a) 328 m
6.1
1. a) No, the angle is coming down from the y axis.
c) No, the angle is coming from a terminal arm.
2. a)The sketch is in quadrant I
3. a) 𝑠𝑖𝑛60 =
√3
2
√3 1
b) 𝑟 = √89
1
𝑐𝑜𝑠60 = 2
√2 √2
)
2
3. a) 82.42 m b) 167.58 m c) 79.9°
b) 817 m
b) The angle is coming up from the x-axis
d) No the angle is coming from a terminal arm.
c) 𝑠𝑖𝑛𝜃 =
8√89
89
𝑐𝑜𝑠𝜃 =
1
𝑡𝑎𝑛60 = √3 b) 𝑠𝑖𝑛30 = 2
1 √3
)
2
4. a) ( 2 , 2)
b) ( 2 ,
c) (2 ,
7. a)i)2√13
ii) √58
b)i) 𝑠𝑖𝑛𝜃 =
5. A) 18.0 m
3√13
, 𝑐𝑜𝑠𝜃
13
=
3√58
7√58
3
, 𝑐𝑜𝑠𝜃 = 58 , 𝑡𝑎𝑛𝜃 = 7 , 𝜃 = 23°
58
12
12
√5
, 𝑡𝑎𝑛𝜃 = 5
b) 𝑐𝑜𝑠𝜃 = 5 , 𝑡𝑎𝑛𝜃 = 2
13
5√89
89
cos 30 =
b) 34°
2√13
, 𝑡𝑎𝑛𝜃
13
𝑡𝑎𝑛𝜃 =
√3
2
8
5
𝑡𝑎𝑛30 =
6.a) (9.4, 3.4)
3
= 2,
d) 𝜃 = 58°
√3
3
b) (0.9, 4.9)
𝜃 = 56°
b) ii) 𝑠𝑖𝑛𝜃 =
8. a) 𝑠𝑖𝑛𝜃 =
9. 20 km [N]
3
c) 𝑠𝑖𝑛𝜃 = 4 , 𝑐𝑜𝑠𝜃 =
√7
4
3 km [E]
Math 20-1 Unit 6: Trigonometry Practice Booklet
Page 21
6.2
1. a)
b)
c)
d)
2ai) 34°
ii) 82°
iii) 61°
iv) 70°
bi) 146°, 214°, 326°
bii) 82°, 262°, 278°
biii) 61°, 119°, 299°
biv) 70°, 110°, 250°
3. a) IV
b) I
c) III
d) II
4. a) II, III
b) II, IV
c) I, II
d) I, III
−3
4
−4
5. a) In quadrant II
b) 5
c) 𝑐𝑜𝑠𝜃 = 5 , 𝑠𝑖𝑛𝜃 = 5 , 𝑡𝑎𝑛𝜃 = 3
d) 𝜃𝑟 = 53°, 𝜃𝑠 = 127°
−3
−4
4
6. a) 𝑐𝑜𝑠𝜃 = 5 , 𝑠𝑖𝑛𝜃 = 5 , 𝑡𝑎𝑛𝜃 = 3 , 𝜃 = 233°
c) 𝑐𝑜𝑠𝜃 = 0, 𝑠𝑖𝑛𝜃 = 2, 𝑡𝑎𝑛𝜃 = 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑, 𝜃 = 90°
8. a) 𝑡𝑎𝑛 ∝= √17
c) 𝜃 = 90°
10. a) 27°, 207°
12. 𝑠𝑖𝑛𝜃 =
−3√7
, 𝑐𝑜𝑠𝜃
8
3√58
b) 𝑠𝑖𝑛 ∝= 58
d) 𝜃 = 0°, 180°, 360°
b) 53°, 307°
1
= 8 , 𝑡𝑎𝑛𝜃 = −3√7
b) 𝑐𝑜𝑠𝜃 = −6, 𝑠𝑖𝑛𝜃 = 0, 𝑡𝑎𝑛𝜃 = 0, 𝜃 = 180°
7. 14 km
9. a) 𝜃 = 45°, 𝜃 = 225°
e) 𝜃 = 0°, 360°
11. D
b) 𝜃 = 0°, 180°, 360°
f) 𝜃 = 90°, 270°
13. A
6.3
1. a) 𝑏 = 2.5 𝑐𝑚
b) 𝑏 = 6.5 𝑐𝑚 2. a) < 𝐸 = 49°, < 𝐸 = 39° 3. a) 𝑀𝑁 = 7.9 𝑐𝑚 b) 𝑀𝑁 = 23.3 𝑐𝑚
4. a) No, you don’t know an angle opposite of c or a
b) No, you do not know any angles.
c) Yes, the angle opposite h is 70°
d) Yes, Find <N then 180-48-<N
5. a)𝐽𝐺 = 359 𝑐𝑚, 𝐻𝐺 = 161𝑐𝑚
b) 790 𝑐𝑚
6. 𝑅𝑄 = 5.8 𝑐𝑚
< 𝑃 = 58°, < 𝑄 = 48°
7. 5.4 km
8. a) 1109 m and 810 m
b) 520 m
9. 12.7 km
10. 98.1 cm
6.4
1. Cosine Law: 𝑏 = 6.3 𝑐𝑚
b)Trig Ratio: 𝑑 = 7.9𝑐𝑚
c)sine law: 𝜃 = 34° d) sine law: 𝑘 = 14.8 𝑐𝑚
2. a) 𝑞 = 24.0 𝑚
b) 𝑢 = 42.3 𝑐𝑚
c) 𝜃 = 68°
3.a) < 𝐶 = 64°, < 𝐷 = 86°, < 𝐵 = 30°
b) 𝑀𝑁 = 36.3 𝑚, < 𝑀 = 54°, < 𝑁 = 23°
4. 𝐴𝐵 = 2√7 𝑐𝑚, 𝐵𝐶 = 4√7𝑐𝑚
5. 26.8 𝑐𝑚2
6. a) 6.8 𝑘𝑚 b) 39° 𝑁𝑜𝑟𝑡ℎ 𝑜𝑓 𝐸𝑎𝑠𝑡
7. 14.8 cm
Practice Test:
1. B
2. C
12. B
13. D
3. A 4. B 5. C
14. A
15. 6.6
Math 20-1 Unit 6: Trigonometry Practice Booklet
6. A 7. D
16. 51
8. D 9. C
17. D
18. 39
10. D
19. D
11. 268
20. 8.0
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