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Math 10 Foundations LG 15 Practice Quiz 3


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

 1. 
Determine tan A and tan C.
mc001-1.jpg
a.
tan A = 1.25; tan C = 0.8
c.
tan A = 0.8; tan C = 1.25
b.
tan A = 0.8; tan C = 0.7809...
d.
tan A = 0.6247...; tan C = 1.25
 

 2. 
Determine the measure of ÐD to the nearest tenth of a degree.
mc002-1.jpg
a.
18.4°
b.
19.5°
c.
70.5°
d.
71.6°
 

 3. 
Determine the measure of ÐDBC to the nearest tenth of a degree.
mc003-1.jpg
a.
27.5°
b.
24.8°
c.
65.2°
d.
62.5°
 

 4. 
A ladder leans against the side of a building. The top of the ladder is 5 m from the ground. The base of the ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground?
a.
79°
b.
11°
c.
9°
d.
83°
 

 5. 
Determine the length of side l to the nearest tenth of a metre.
mc005-1.jpg
a.
5.4 m
b.
27.4 m
c.
11.1 m
d.
5.0 m
 

 6. 
Determine the length of side s to the nearest tenth of a millimetre.
mc006-1.jpg
a.
18.4 mm
b.
43.5 mm
c.
8.6 mm
d.
9.5 mm
 

 7. 
A guy wire is attached to a tower at a point that is 5.5 m above the ground. The angle between the wire and the level ground is 56°. How far from the base of the tower is the wire anchored to the ground, to the nearest tenth of a metre?
a.
3.1 m
b.
6.6 m
c.
3.7 m
d.
8.2 m
 

 8. 
The angle of inclination of a solar panel on the roof of a cottage is 57°. Determine the height of the roof, to the nearest tenth of a metre.
mc008-1.jpg
a.
3.8 m
b.
4.9 m
c.
2.1 m
d.
5.9 m
 

 9. 
A road has an angle of inclination of 16°. Determine the increase in altitude of the road, to the nearest metre, for every 150 m of horizontal distance.
a.
523 m
b.
144 m
c.
43 m
d.
41 m
 

 10. 
A surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the base of a tower. The angle between the horizontal and the line of sight to the top of the tower was 21°. Determine the height of the tower to the nearest tenth of a metre.
a.
157.8 m
b.
23.0 m
c.
24.5 m
d.
65.8 m
 

 11. 
Determine sin A and cos A to the nearest tenth.
mc011-1.jpg
a.
sin A = 1.7;  cos A = 0.8
c.
sin A = 0.6;  cos A = 1.3
b.
sin A = 0.8;  cos A = 0.6
d.
sin A = 0.6;  cos A = 0.8
 

 12. 
Determine the measure of ÐV to the nearest tenth of a degree.
mc012-1.jpg
a.
59.5°
b.
36.1°
c.
30.5°
d.
53.9°
 

 13. 
A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?
a.
33.3°
b.
61.3°
c.
56.7°
d.
28.7°
 

 14. 
Determine the length of XY to the nearest tenth of a centimetre.
mc014-1.jpg
a.
8.4 cm
b.
15.2 cm
c.
31.4 cm
d.
19.9 cm
 

 15. 
Determine the length of RS to the nearest tenth of a metre.
mc015-1.jpg
a.
19.7 m
b.
5.7 m
c.
18.0 m
d.
64.3 m
 

 16. 
Solve this right triangle. Give the measures to the nearest tenth.
mc016-1.jpg
a.
mc016-2.jpg m
c.
mc016-4.jpg m
b.
mc016-3.jpg m
d.
mc016-5.jpg m
 

 17. 
A water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. It then travels 15 km due east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the path it took due east and the path it will take to return directly to its dock?
a.
25°
b.
62°
c.
28°
d.
65°
 

 18. 
Calculate the measure of ÐGHJ to the nearest tenth of a degree.
mc018-1.jpg
a.
mc018-2.jpg°
b.
29.3°
c.
mc018-3.jpg°
d.
68.0°
 

 19. 
From the top of a 25-m lookout tower, a fire ranger observes one fire due east of the tower at an angle of depression of 7°. She sees another fire due north of the tower at an angle of depression of 3°. How far apart are the fires to the nearest metre?
a.
205 m
b.
681 m
c.
477 m
d.
519 m
 

 20. 
Calculate the measure of ÐABC to the nearest tenth of a degree.
mc020-1.jpg
a.
mc020-2.jpg°
b.
102.5°
c.
77.5°
d.
mc020-3.jpg°
 

Short Answer
 

 21. 
Determine the length of side r to the nearest tenth of a metre.

sa021-1.jpg
 

 22. 
A rectangle has length 19.0 cm. The angle between one shorter side of the rectangle and a diagonal is 56°. Calculate the width of the rectangle, to the nearest tenth of a centimetre.
 

 23. 
Determine the length of RT to the nearest tenth of a metre.
sa023-1.jpg
 

 24. 
A guy wire supports a flagpole. The wire is anchored 8 ft. from the base of the pole and the angle of inclination of the wire is 47°. Calculate the length of the wire to the nearest foot.
 

 25. 
From the roof of Yee’s building, the angle of elevation of the top of a taller building is 37°. The angle of depression of the base of the building is 28°. The buildings are 21 m apart. Determine the height of the taller building to the nearest metre.
 

Problem
 

 26. 
A rectangle measures 7.9 cm by 5.2 cm. Determine the measure, to the nearest degree, of the acute angles formed by the intersection of the diagonals.
 

 27. 
A boat was docked 30.0 m from the base of a cliff. A sailor used a clinometer to sight the top of the cliff. The angle between the horizontal and the line of sight was 74°. The sailor held the clinometer 1.5 m above the surface of the water. Determine the height of the cliff to the nearest tenth of a metre.
 

 28. 
Calculate the angle of inclination of the roof to the nearest tenth of a degree.
pr028-1.jpg
 

 29. 
Solve DLMN. Give the measures to the nearest tenth. Explain your strategy.
pr029-1.jpg
 

 30. 
Determine the area of this triangle to the nearest tenth of a square centimetre.
pr030-1.jpg
 



 
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