Assignment Previewer ...smithies/TrigPostF17/TrigT3PracBSoln.pdf · The Law of Cosines can be used...
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Description
This is practice test B to help prepare for Test 3. It covers sections 3.1, 3.2 and 3.3.
Part A covers sections 2.4 and 2.5.
Practice Test 3 B - Sections 3.1 and 3.2 (11634927)
1. -Question Details LarTrig9 3.1.004. [2447154]
Fill in the blank.
The area of an oblique triangle is given by ________.bc sin A = ab sin C =12
12
ac sin B12
bc sin C12
ac sin C12
ab sin B12
ac sin A12
2. -Question Details LarTrig9 3.1.005. [2483694]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
A= 31 °
a = 14.57
c = 27.44
3. -Question Details LarTrig9 3.1.011. [2447016]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
B= 41.77 °
a = 20.42
b = 13.76
A = 81° 20', C = 56.9°, c = 17.3
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4. -Question Details LarTrig9 3.1.017. [2447191]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
B = 22.02 °
C= 127.98 °
c = 12.61
A = 30°, a = 8, b = 6
5. -Question Details LarTrig9 3.1.018. [3221050]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
Case 1: Case 2:
C = 62.54 ° (smaller C-value) C = 117.46 ° (larger C-value)
B = 64.46 ° B = 9.54 °
b = 10.17 b = 1.87
A = 53°, a = 9, c = 10
6. -Question Details LarTrig9 3.1.019. [2446472]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
A = 22.90 °
C= 136.60 °
c = 17.66
B = 20° 30', a = 10, b = 9
7. -Question Details LarTrig9 3.1.021. [2447342]
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
B = 14.52 °
C= 22.48 °
c = 7.62
A = 143°, a = 12, b = 5
8. -Question Details LarTrig9 3.1.025. [2446397]
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal
places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
B = 48.39 °
C= 19.61 °
c = 44.88
A = 112°, a = 124, b = 100
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9. -Question Details LarTrig9 3.1.026.MI. [2548291]
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal
places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
B = IMPOSSIBLE °
C= IMPOSSIBLE °
c = IMPOSSIBLE
Solution or Explanation
Given:
No triangle is formed because A is obtuse and a < b.
A = 100°, a = 195, b = 280
a = 195, b = 280, A = 100°
10. -Question Details LarTrig9 3.1.027. [2446147]
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal
places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
B = IMPOSSIBLE °
C= IMPOSSIBLE °
c = IMPOSSIBLE
A = 79°, a = 18, b = 19
11. -Question Details LarTrig9 3.1.029. [2446445]
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal
places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
Case 1: Case 2:
B = 58.20 ° (smaller B-value) B = 121.80 ° (larger B-value)
C = 67.80 ° C = 4.20 °
c = 11.33 c = 0.90
A = 54°, a = 9.9, b = 10.4
12. -Question Details LarTrig9 3.1.039. [2446461]
Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)
19.5
C = 120°, a = 5, b = 9
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13. -Question Details LarTrig9 3.1.040. [2446820]
Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)
B = 139°, a = 89, c = 37
1080.2
Solution or Explanation
Area = ac sin(B) = (89)(37) sin(139°) ≈ 1080.212
12
14. -Question Details LarTrig9 3.1.042. [2447324]
Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)
33.7
C = 167°, a = 15, b = 20
15. -Question Details LarTrig9 3.1.047. [2447298]
Because of prevailing winds, a tree grew so that it was leaning 2° from the vertical. At a point d = 44 meters from the tree,
the angle of elevation to the top of the trees is a = 27° (see figure). Find the height h of the tree. (Round your answer to one
decimal place.)
h = 22.8 m
Solution or Explanation
C = 180° − 27° − 92° = 61°
h = sin(27°) ≈ 22.8 meters44sin(61°)
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16. -Question Details LarTrig9 3.1.050.MI. [3179078]
A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S
41° W. From a tree x = 110 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E,
respectively. Find the distance from the gazebo to the dock. (Round your answer to the nearest whole number.)
85 m
Solution or Explanation
Given: x = 110
A = 74° − 28° = 46°
B = 180° − 41° − 74° = 65°
C = 180° − 46° − 65° = 69°
a = sin A = sin 46° ≈ 85 metersxsin C
110sin 69°
17. -Question Details LarTrig9 3.1.054. [2446427]
The angles of elevation to an airplane from two points A and B on level ground are 55° and 76°, respectively. The points A
and B are 2.7 miles apart, and the airplane is east of both points in the same vertical plane. Find the altitude of the plane.
(Round your answer to two decimal places.)
5.99 mi
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18. -Question Details LarTrig9 3.1.056. [2446096]
The Leaning Tower of Pisa in Italy leans because it was built on unstable soil—a mixture of clay, sand, and water. The tower is
approximately 58.36 meters tall from its foundation (see figure). The top of the tower leans about 5.45 meters off center.
(a) Find the angle of lean α of the tower. (Round your answer to two decimal places.)
5.36 °
(b) Write β as a function of d and θ, where θ is the angle of elevation to the sun.
β =
(c) Use the Law of Sines to write an equation for the length d of the shadow cast by the tower in terms of θ.
d =
(d) Use a graphing utility to complete the table. (Round your answers to two decimal places.)
θ 10° 20° 30°
d 324.08 m 154.19 m
θ 40° 50° 60°
d 63.80 m 43.30 m
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19. -Question Details LarTrig9 3.1.062. [3190199]
In the figure, a triangle is to be formed by drawing a line segment of length a from (x, y) = (20, 15) to the positive x-axis. For
what value(s) of a can you form one triangle, two triangles, and no triangles?
(a) one triangle
(b) two triangles
(c) no triangles
a ≥ 25, a = 15
a ≥ 20
a ≥ 25
a ≥ 15
a > 20, a = 15
20 < a < 25
15 < a < 20
15 < a < 25
a > 15
0 < a < 25
a = 15
0 < a ≤ 15
0 < a < 25
0 < a < 20
0 < a < 15
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20. -Question Details LarTrig9 3.2.001. [2446954]
Fill in the blank.
When you are given three sides of a triangle, you use the Law of ---Select--- Cosines to find the three
angles of the triangle.
21. -Question Details LarTrig9 3.2.004. [2548247]
Fill in the blank.
The Law of Cosines can be used to establish a formula for finding the area of a triangle called
---Select--- Heron's Formula.
Solution or Explanation
Heron's Formula
22. -Question Details LarTrig9 3.2.005. [2446739]
Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.
A= 22.33 °
B= 27.13 °
C= 130.54 °
23. -Question Details LarTrig9 3.2.006. [2548297]
Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.
A = 32.09 °
B = 20.74 °
C= 127.17 °
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24. -Question Details LarTrig9 3.2.012. [2446413]
Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.
A= 42.85 °
B= 25.15 °
c= 10.91
25. -Question Details LarTrig9 3.2.018. [3738306]
Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.
A = 51°, b = 5, c = 15
a = 12.47
B = 18.15 °
C = 110.85 °
26. -Question Details LarTrig9 3.2.025. [3220083]
Complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d.
Round your answers to two decimal places.)
a b c d θ ϕ
3 9 11.69 6.58 30° 150.00 °
Solution or Explanation
d2 = 32 + 92 − 2(3)(9)cos(30°) ≈ 43.2346 d ≈ 6.58
2ϕ = 360° − 2(30°) = 300° ϕ = 150°
c2 = 32 + 92 − 2(3)(9)cos(150°) ≈ 136.7654 c ≈ 11.69
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27. -Question Details LarTrig9 3.2.026. [3220280]
Complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d.
Round your answers to two decimal places.)
a b c d θ ϕ
26
42
60.51
34.91
56.00
°
124°
28. -Question Details LarTrig9 3.2.031. [2447069]
Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.
Solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not
possible, enter IMPOSSIBLE in each corresponding answer blank.)
A= 117.73 °
C= 26.27 °
b= 3.98
a = 6, c = 3, B = 36°
Law of Sines
Law of Cosines
29. -Question Details LarTrig9 3.2.033. [2446258]
Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.
Solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not
possible, enter IMPOSSIBLE in each corresponding answer blank.)
B= IMPOSSIBLE °
C= IMPOSSIBLE °
c= IMPOSSIBLE
A = 26°, a = 3, b = 16
Law of Sines
Law of Cosines
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30. -Question Details LarTrig9 3.2.037. [2446266]
Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.)
36.66
a = 5, b = 17, c = 20
31. -Question Details LarTrig9 3.2.038.MI. [2446731]
Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.)
a = 33, b = 36, c = 25
399.04
Solution or Explanation
a = 33, b = 36, c = 25
s =
=
= 47
a + b + c2
33 + 36 + 252
Area =
=
≈ 399.04
s(s − a)(s − b)(s − c)
47(14)(11)(22)
32. -Question Details LarTrig9 3.2.047.MI. [2446909]
To approximate the length of a marsh, a surveyor walks x = 380 meters from point A to point B, then turns 75° and walks
220 meters to point C (see figure). Approximate the length AC of the marsh. (Round your answer to one decimal place.)
485.9 m
Solution or Explanation
b2 = 2202 + 3802 − 2(220)(380)cos 105° b ≈ 485.9 meters
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Name (AID): Practice Test 3 B - Sections 3.1 and 3.2 (11634927)
Submissions Allowed: 5
Category: Homework
Code:
Locked: No
Author: Smithies, Laura ( [email protected] )
Last Saved: Nov 18, 2017 08:49 PM EST
Permission: Protected
Randomization: Person
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Assignment Details
33. -Question Details LarTrig9 3.2.048. [2447410]
Determine the angle θ in the design of the streetlight shown in the figure, where x = 1.9. (Round your answer to one decimal
place.)
θ = 132.1 °
Solution or Explanation
cos(θ) = ≈ -0.67018
θ ≈ 132.1°
1.92 + 32 − (4.5)2
2(1.9)(3)
34. -Question Details LarTrig9 3.2.051. [2447309]
On a map, Minneapolis is 165 millimeters due west of Albany, Phoenix is 216 millimeters from Minneapolis, and Phoenix is
368 millimeters from Albany (see figure). (Round your answers to one decimal place.)
(a) Find the bearing of Minneapolis from Phoenix.
N 59.7 ° E
(b) Find the bearing of Albany from Phoenix.
N 72.8 ° E
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