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Math 11 Foundations LG 10 Unit 2 Practice Test #5


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

 1. 
Which ratios are equivalent for all three side-angle pairs in acute triangles?
a.
mc001-1.jpg
b.
mc001-2.jpg
c.
mc001-3.jpg
d.
mc001-4.jpg
 

 2. 
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
 

 3. 
In DUVW, ÐU = 50°, v = 19.4 cm, and ÐV = 45°.
Determine the length of side u to the nearest tenth of a centimetre.
a.
20.0 cm
b.
18.0 cm
c.
21.0 cm
d.
19.0 cm
 

 4. 
In DXYZ, ÐX = 51°, x = 7.0 cm, and ÐZ = 41°.
Determine the length of side y to the nearest tenth of a centimetre.
a.
11.0 cm
b.
10.0 cm
c.
9.0 cm
d.
8.0 cm
 

 5. 
In DABC, a = 4.1 cm, b = 4.4 cm, and ÐB = 64°.
Determine the measure of ÐC to the nearest degree.
a.
59°
b.
57°
c.
61°
d.
55°
 

 6. 
Determine the length of EF to the nearest centimetre.

mc006-1.jpg
a.
84 cm
b.
82 cm
c.
88 cm
d.
86 cm
 

 7. 
Determine the length of KL to the nearest centimetre.

mc007-1.jpg
a.
27 cm
b.
26 cm
c.
34 cm
d.
33 cm
 

 8. 
Determine the measure of q to the nearest degree.

mc008-1.jpg
a.
88°
b.
86°
c.
84°
d.
90°
 

 9. 
In DDEF, d = 13.5 cm, e = 18.2 cm, and ÐF = 60°.
Determine the measure of f to the nearest tenth of a centimetre.
a.
17.0 cm
b.
16.4 cm
c.
16.6 cm
d.
16.8 cm
 

 10. 
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°
 

 11. 
In a parallelogram, two adjacent sides measure 20 cm and 27 cm.
The shorter diagonal is 23 cm. Determine, to the nearest degree,
the measures of the larger angles in the parallelogram.
a.
103°
b.
113°
c.
134°
d.
124°
 

 12. 
Which pair of angles have the tangent ratio 0.60?
a.
53°, 127°
b.
27°, 153°
c.
0°, 180°
d.
none of the above
 

 13. 
Which law could you use to determine the unknown angle in this triangle?
mc013-1.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
 

 14. 
Which set of measurements can produce two possible triangles?
a.
ÐA = 28°, a = 10.5 m, b = 15.0 m
b.
ÐA = 28°, a = 7.0 m, b = 15.0 m
c.
ÐA = 28°, a = 16.0 m, b = 15.0 m
d.
ÐA = 28°, a = 5.5 m, b = 15.0 m
 

 15. 
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
 

 16. 
In DXYZ, ÐY = 29°, x = 15.4 m, and y = 12.0 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.
 

 17. 
In DFGH, GH = 4.5 cm and G = 15°.
What is the height of the triangle from base GF?
a.
1.5 cm
b.
1.3 cm
c.
1.2 cm
d.
0.9 cm
 

 18. 
In DKLM, LM = 16.0 cm and ÐL = 36°.
What is the height of the triangle from base LK?
a.
9.4 cm
b.
9.2 cm
c.
8.7 cm
d.
8.5 cm.
 

 19. 
Which would you use to determine the indicated angle measure?
mc019-1.jpg
a.
primary trigonometric ratios
b.
the sine law only
c.
the cosine law only
d.
the sine law or the cosine law
 

 20. 
Determine the indicated angle measure to the nearest degree.
mc020-1.jpg
a.
40°
b.
42°
c.
44°
d.
46°
 

Short Answer
 

 21. 
Sketch a triangle that corresponds to the equation.
Then, determine the third angle measure and the third side length.

sa021-1.jpg
 

 22. 
Determine the measure of q to the nearest degree.

sa022-1.jpg
 

 23. 
In DXYZ, ÐX = 36°, x = 14.4 cm, and ÐY = 70°.
Determine the length of side y to the nearest tenth of a centimetre.
 

 24. 
In a parallelogram, two adjacent sides measure 8.4 cm and 7.2 cm. The shorter diagonal is 10.5 cm. Determine, to the nearest degree, the measures of the larger angles in the parallelogram.
 

 25. 
Determine two angles between 0° and 180° that have the sine ratio 0.8480.
 

Problem
 

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

 27. 
A bush pilot delivers supplies to a remote camp by flying 200 km in the direction N47°E. While at the camp, the pilot receives a radio message to pick up a passenger at a village. The village is 105 km S21°E from the camp. The pilot collects the passenger and flies back to his starting point. What is the total distance that the pilot has flown, to the nearest kilometre?
 

 28. 
In DQRS, q = 1.7 m, r = 4.3 m, and s = 5.6 m. Solve DQRS by determining the measure of each angle to the nearest degree. Show your work and draw DQRS.
 

 29. 
A landowner claims that her property is triangular, with one side 400 m long and another side 250 m long. The opposite angle to the 250 m side measures 30°. Determine two possible lengths of the third side, to the nearest metre. Show your work.
 

 30. 
A surveyor is measuring the length of a lake. He takes angle measurements from two positions, A and B, that are 436 m apart, and on opposite sides of the lake. From B, the measure of the angle between the sight lines to the ends of the lake is 120°, and the measure of the angle between the sight lines to A and one end of the lake is 105°. From A, the measure of the angle between the sight lines to the ends of the lake is 50°, and the measure of the angle between the sight lines to B and the same end of the lake is 16°. Calculate the length of the lake, to the nearest metre. Show your work.
 



 
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