Name: 
 

Math 11 Foundations LG 10 Unit 2 Practice Test #1


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Determine the length of c to the nearest tenth of a centimetre.

mc001-1.jpg
a.
23.0 cm
b.
25.0 cm
c.
24.0 cm
d.
26.1 cm
 

 2. 
Determine the length of f to the nearest tenth of a centimetre.

mc002-1.jpg
a.
78.6 cm
b.
79.0 cm
c.
79.4 cm
d.
78.2 cm
 

 3. 
Determine the measure of q to the nearest degree.

mc003-1.jpg
a.
39°
b.
44°
c.
34°
d.
49°
 

 4. 
In DRST, ÐS = 54°, s = 91.8 cm, and ÐT = 64°.
Determine the length of side t to the nearest tenth of a centimetre.
a.
102.4 cm
b.
102.2 cm
c.
102.0 cm
d.
102.6 cm
 

 5. 
In DDEF, d = 10.0 cm, e = 8.6 cm, and ÐE = 45°.
Determine the measure of ÐD to the nearest degree.
a.
35°
b.
55°
c.
45°
d.
65°
 

 6. 
In DQRS, q = 10.0 cm, s = 9.0 cm, and ÐS = 61°.
Determine the measure of ÐQ to the nearest degree.
a.
76°
b.
75°
c.
78°
d.
77°
 

 7. 
What information do you need to know about an acute triangle to use the cosine law?
a.
two sides and any angle
b.
two angles and any side
c.
all the angles
d.
all the sides
 

 8. 
Determine the length of PQ to the nearest tenth of a centimetre.

mc008-1.jpg
a.
9.4 cm
b.
9.1 cm
c.
8.5 cm
d.
8.8 cm
 

 9. 
In DDEF, d = 23.9 cm, e = 16.8 cm, and f = 27.0 cm.
Determine the measure of ÐD to the nearest degree.
a.
54°
b.
64°
c.
58°
d.
61°
 

 10. 
Which one of the following equations is valid?
a.
sin 45° = –sin 135°
b.
sin 45° = sin 135°
c.
sin 45° = –sin 45°
d.
none of the above
 

 11. 
Which one of the following equations is valid?
a.
cos 36° = –cos 144°
b.
cos 36° = –cos 36°
c.
cos 36° = cos 144°
d.
none of the above
 

 12. 
Calculate sin 16° to four decimal places. Predict another term that equals sin 16°.
a.
–0.2756; sin 164°
b.
0.2576; sin 164°
c.
 0.2756; –sin 16°
d.
none of the above
 

 13. 
Which law could you use to determine the unknown side length in this triangle?
mc013-1.jpg
a.
neither the sine law nor the cosine law
b.
the sine law only
c.
the cosine law only
d.
the sine law and the cosine law
 

 14. 
Which law could you use to determine the unknown angle in this triangle?
mc014-1.jpg
a.
the sine law only
b.
neither the sine law nor the cosine law
c.
the cosine law only
d.
the sine law and the cosine law
 

 15. 
Determine the unknown side length to the nearest centimetre.
mc015-1.jpg
a.
11.4 cm
b.
10.8 cm
c.
12.0 cm
d.
12.2 cm
 

 16. 
Which set of measurements will produce one right triangle with b as the hypotenuse?
a.
ÐA = 60°, a = 10.4 m, b = 12.0 m
b.
ÐA = 60°, a = 11.6 m, b = 12.0 m
c.
ÐA = 60°, a = 8.7 m, b = 12.0 m
d.
ÐA = 60°, a = 14.5 m, b = 12.0 m
 

 17. 
Which set of measurements will produce just one triangle?
a.
ÐA = 25°, a = 9.4 m, b = 10.0 m
b.
ÐA = 40°, a = 9.4 m, b = 10.0 m
c.
ÐA = 125°, a = 9.4 m, b = 10.0 m
d.
ÐA = 70°, a = 9.4 m, b = 10.0 m
 

 18. 
Which set of measurements can produce two possible triangles?
a.
ÐA = 48°, a = 4.2 m, b = 5.0 m
b.
ÐA = 48°, a = 8.2 m, b = 13.0 m
c.
ÐA = 48°, a = 5.2 m, b = 7.0 m
d.
ÐA = 35°, a = 10.8 m, b = 8.0 m
 

 19. 
In DJKL, ÐJ = 115°, k = 6.2 m, and j = 5.5 m.
Which statement is true for this set of measurements?
a.
This is not a SSA situation.
b.
This is a SSA situation; no triangle is possible.
c.
This is a SSA situation; only one triangle is possible.
d.
This is a SSA situation; two triangles are possible.
 

 20. 
Determine the indicated angle measure to the nearest degree.
mc020-1.jpg
a.
98°
b.
100°
c.
102°
d.
cannot be determined
 

Short Answer
 

 21. 
How long, to the nearest inch, is the right rafter in the roof shown?
sa021-1.jpg
 

 22. 
Determine the unknown angle measure to the nearest degree.
sa022-1.jpg
 

 23. 
Determine the unknown angle measure to the nearest degree.
sa023-1.jpg
 

 24. 
In DPQR, ÐP = 36°, p = 9.0 cm, and q = 6.5 cm. Does this involve the SSA situation? If so, how many triangles with the given measurements are possible? Draw the triangle(s) to support your answer.
 

 25. 
What law or property would you use to determine the indicated angle measure?
sa025-1.jpg
 

Problem
 

 26. 
Determine the perimeter of the triangle to the nearest tenth of a centimetre.
pr026-1.jpg
 

 27. 
A building is observed from two points, P and Q, that are 134.0 m apart. The angle of elevation is 35° at P and 27° at Q. Sketch the situation. Determine the height of the building to the nearest tenth of a metre.
 

 28. 
A farmer finishes repairing a fence post and then walks 180 yd through her corn field. She turns and walks another 240 yd west, until she can see the fence post directly southeast of her. She realizes that she left some of her tools at the fence post and heads directly back to it. How far does she need to walk, to the nearest metre?
 

 29. 
Two forest-fire towers, A and B, are 18.9 km apart. From tower A, the compass heading for tower B is S78°E. The ranger in each tower sees the same forest fire. The heading of the fire from tower A is N43°E. The heading of the fire from tower B is N48°W. How far, to the nearest tenth of a kilometre, is the fire from each tower? Include a rough sketch in your solution.
 

 30. 
Two forest-fire towers, A and B, are 5.4 km apart. From tower A, the compass heading for tower B is S62°E. The ranger in each tower sees the same forest fire. The heading of the fire from tower A is N78°E. The heading of the fire from tower B is N42°W. How far, to the nearest tenth of a kilometre, is the fire from each tower? Include a rough sketch in your solution.
 



 
Check Your Work     Start Over