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MATH1720HomeworkChapter2Section4

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

 1. 
The number represents an approximate measurement. State the range represented by the measurement.
21 ft
a.
20.9 ft to  21.1 ft
c.
20.5 ft to  21.5 ft
b.
20.75 ft to  21.25 ft
d.
20 ft to  22 ft
 

 2. 
The number represents an approximate measurement. State the range represented by the measurement.
17.3 m
a.
17.25 m to  17.35 m
c.
16.3 m to  18.3 m
b.
17.29 m to  17.31 m
d.
17.275 m to  17.325 m
 

 3. 
The number represents an approximate measurement. State the range represented by the measurement.
24.35 k
a.
24.3475 kg to  24.3525 kg
c.
24.345 kg to  24.355 kg
b.
23.35 kg to  25.35 kg
d.
24.349 kg to  24.351 kg
 

 4. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc004-1.jpg

A =  11° mc004-2.jpg, c =  213 ft
Round side lengths to two decimal places.
a.
B =  78° mc004-3.jpg; a =  45.79 ft; b =  209.90 ft
c.
B =  78° mc004-5.jpg; a =  42.02 ft ; b =  207.81 ft
b.
B =  79° mc004-4.jpg; a =  42.59 ft; b =  204.70 ft
d.
B =  78° mc004-6.jpg; a =  42.59 ft; b =  208.70 ft
 

 5. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc005-1.jpg

B =  53°47', b =  25 km
Round side lengths to one decimal place.
a.
A =  36°13'; c =  42.3 km; a =  31.0 km
c.
A =  36°13'; c =  31.0 km; a =  18.3 km
b.
A =  36°13'; c =  42.3 km; a =  18.3 km
d.
A =  36°13'; c =  31.1 km; a =  42.0 km
 

 6. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc006-1.jpg

A =  41.3°, b =  2.5 m
Round side lengths to one decimal place.
a.
B =  48.7°; a =  2.2 m; c =  3.3 m
c.
B =  48.7°; a =  1.1 m; c =  2.7 m
b.
B =  48.7°; a =  1.1 m; c =  4.0 m
d.
B =  48.7°; a =  4.0 m; c =  4.7 m
 

 7. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc007-1.jpg

B = 65.4834°, c =  3618.6 m
Give side lengths to two decimal places.
a.
A = 24.5166°; a =  1416.68 m; b =  3277.05 m
b.
A = 24.5166°; a =  1501.56 m; b =  3246.96 m
c.
A = 24.5166°; a =  1501.56 m; b =  3292.35 m
d.
A = 24.5166°; a =  1560.70 m; b =  3292.35 m
 

 8. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc008-1.jpg

B = 58.45°, a =  434.7 m
Give side lengths to two decimal places.
a.
A = 31.55°; b =  664.51 m; c =  830.78 m
c.
A = 31.55°; b =  707.98 m; c =  843.43 m
b.
A = 31.55°; b =  751.45 m; c =  817.21 m
d.
A = 31.55°; b =  707.98 m; c =  830.78 m
 

 9. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc009-1.jpg

a =  10.9 cm, b =  21.7 cm
Round the missing side length to one decimal place.
a.
A =  26° 40'; B =  63° 20'; c =  25.8 cm
c.
A =  30° 9'; B =  59° 51'; c =  24.3 cm
b.
A =  30° 9'; B =  59° 51'; c =  22.6 cm
d.
A =  26° 40'; B =  63° 20'; c =  24.3 cm
 

 10. 
Solve the right triangle.  If two sides are given, give angles in degrees and minutes.

mc010-1.jpg

a =  50.26 ft, c =  231 ft
Round the missing side length to two decimal places.
a.
A =  13° mc010-2.jpg, B =  76° mc010-3.jpg, b = 225.47 ft
c.
A =  12° mc010-6.jpg, B =  77° mc010-7.jpg, b =209.69 ft
b.
A =  10° mc010-4.jpg, B =  79° mc010-5.jpg, b = 236.74 ft
d.
A =  12° mc010-8.jpg; B =  77° mc010-9.jpg; b =  225.47 ft
 

 11. 
Solve the right triangle.
 a =  2.6 cm, b =  1.3 cm, C = 90°
Round values to one decimal place.
a.
A =  26.6°, B =  63.4°, c =  2.9 cm
c.
A =  30.0°, B =  60.0°, c =  3.9 cm
b.
A =  63.4°, B =  26.6°, c =  2.9 cm
d.
A =  58.9°, B =  31.1°, c =  2.9 cm
 

 12. 
Solve the right triangle.
 a =  3.6 m, B =  30.3°, C = 90°
Round values to one decimal place.
a.
A =  59.7°, b =  4.4 m, c =  5.7 m
c.
A =  59.7°, b =  2.1 m, c =  4.2 m
b.
A =  59.7°, b =  4.4 m, c =  4.2 m
d.
A =  59.7°, b =  1 m, c =  3.7 m
 

 13. 
Solve the right triangle.
 a =  2.6 in., A =  49.8°, C = 90°
Round values to one decimal place.
a.
b =  4.0 in., B =  40.2°, c =  3.4 in.
c.
b =  2.2 in., B =  40.2°, c =  3.4 in.
b.
b =  4.0 in., B =  40.2°, c =  4.8 in.
d.
b =  1.1 in., B =  40.2°, c =  2.8 in.
 

 14. 
Solve the right triangle.
B =  25.9°, c =  4.1 mm, C = 90°
Round values to one decimal place.
a.
a =  1.8 mm, A =  64.1°, b =  3.7 mm
c.
a =  2.9 mm, A =  64.1°, b =  2.9 mm
b.
a =  3.7 mm, A =  64.1°, b =  1.8 mm
d.
a =  3.7 mm, A =  64.1°, b =  2.9 mm
 

 15. 
Solve the right triangle.
A =  19° mc015-1.jpg, c =  287 ft, C = 90°
Round side lengths to two decimal places, if necessary.
a.
B =  70° mc015-2.jpg, a =  97.98 ft, b =  272.1 ft
c.
B =  70° mc015-4.jpg, a =  94.21 ft , b =  270.01 ft
b.
B =  70° mc015-3.jpg, a =  94.78 ft, b =  270.9 ft
d.
B =  71° mc015-5.jpg, a =  94.78 ft, b =  266.9 ft
 

 16. 
Solve the right triangle.
A =  72° mc016-1.jpg,  c =  278 m , C = 90°
Round side lengths to two decimal places, if necessary.
a.
B =  18° mc016-2.jpg, a =  264.74 m, b =  85.45 m
c.
B =  17° mc016-4.jpg, a =  264.74 m, b =  92.45 m
b.
B =  17° mc016-3.jpg, a =  264.54 m, b =  85.45 m
d.
B =  17° mc016-5.jpg, a =  265.74 m, b =  78.45 m
 

 17. 
On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is mc017-1.jpg long and the shadow is  28 meters, how tall is the flag pole?
a.
45 m
c.
63 m
b.
21 m
d.
49 m
 

 18. 
On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is mc018-1.jpg long and the tree is  32 meters tall, how long is the shadow?
a.
72 m
c.
51 m
b.
64 m
d.
24 m
 

 19. 
To measure the width of a river, a surveyor starts at point A on one bank and walks   74 feet down the river to point B. He then measures the angle ABC to be mc019-1.jpg  Estimate the width of the river to the nearest foot. See the figure below.
      mc019-2.jpg
a.
154 ft
c.
67 ft
b.
35 ft
d.
32 ft
 

 20. 
A conservation officer needs to know the width of a river in order to set instruments correctly for a study of pollutants in the river.  From point A, the conservation officer walks  100 feet downstream and sights point B on the opposite bank to determine that è =  30° (see figure).  How wide is the river (round to the nearest foot)?

      mc020-1.jpg
a.
173 ft
c.
58 ft
b.
115 ft
d.
50 ft
 

 21. 
In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at 0.314 arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 150,000,000 km and è = 0.314 seconds = mc021-1.jpg minutes = mc021-2.jpg degrees, determine the distance d from Earth to 61 Cygni using Bessel's figures. Express the answer in scientific notation.
      mc021-3.jpg
a.
2.28 × mc021-4.jpg km
c.
1.97 × mc021-6.jpg km
b.
9.85 × mc021-5.jpg km
d.
1.05 × mc021-7.jpg km
 

 22. 
A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 235 miles and BC is  625 miles, and if angle C is 90°, find the measure of angle B. Round your answer to the tenths place.
a.
20.6°
c.
34.1°
b.
31.4°
d.
18.7°
 

 23. 
The length of the base of an isosceles triangle is  33.28 meters. Each base angle is  37.57°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.
a.
41.99 m
c.
27.29 m
b.
21.63 m
d.
20.99 m
 

 24. 
From a boat on the lake, the angle of elevation to the top of a cliff is mc024-1.jpg If the base of the cliff is  1683 feet from the boat, how high is the cliff (to the nearest foot)?
a.
397 ft
c.
394 ft
b.
407 ft
d.
404 ft
 

 25. 
From a boat on the river below a dam, the angle of elevation to the top of the dam is mc025-1.jpg If the dam is  1286 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?
a.
4806 ft
c.
4786 ft
b.
4816 ft
d.
4796 ft
 

 26. 
From a balloon  1037 feet high, the angle of depression to the ranger headquarters is mc026-1.jpg How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?
a.
631 ft
c.
626 ft
b.
636 ft
d.
621 ft
 

 27. 
When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is mc027-1.jpg If Joey is known to be standing  32 feet from the base of the tree, how tall is the tree (to the nearest foot)?
a.
40 ft
c.
46 ft
b.
44 ft
d.
42 ft
 

 28. 
From the top of a vertical tower,  319 feet above the the surface of the earth, the angle of depression to a doghouse is mc028-1.jpg How far is it from the doghouse to the foot of the tower? Round your answer to the hundredths place when necessary.
a.
734.11 ft
c.
852.3 ft
b.
749.7 ft
d.
762.1 ft
 

 29. 
A   35-foot ladder is leaning against the side of a building. If the ladder makes an angle of mc029-1.jpg with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place when necessary.
a.
14.33 ft
c.
15.63 ft
b.
20.03 ft
d.
4.96 ft
 

 30. 
A   37-foot ladder is leaning against the side of a building. If the ladder makes an angle of mc030-1.jpgwith the side of the building, how far up from the ground does the ladder make contact with the building? Round your answer to the hundredths place when necessary.
a.
31.16 ft
c.
34.93 ft
b.
36.89 ft
d.
33.73 ft
 

 31. 
A contractor needs to know the height of a building to estimate the cost of a job. From a point mc031-1.jpg away from the base of the building, the angle of elevation to the top of the building is found to be mc031-2.jpg Find the height of the building. Round your answer to the hundredths place when necessary.
a.
80.32 ft
c.
81.85 ft
b.
84.75 ft
d.
86.08 ft
 



 
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