Assignment Previewer ...smithies/TrigPostF17/TrigT3PracBSoln.pdf · The Law of Cosines can be used...

Question 1 2 3 4 5 6 7 8 910111213141516171819202122232425262728293031323334

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


Use the Law of Sines to solve the triangle. Round your answers to two decimal places.

A= 31 °

a = 14.57

c = 27.44



B= 41.77 °

a = 20.42

b = 13.76

A = 81° 20', C = 56.9°, c = 17.3

Assignment Previewer https://www.webassign.net/v4cgi/assignments/pre...

1 of 13 11/20/2017 01:09 PM



B = 22.02 °

C= 127.98 °

c = 12.61

A = 30°, a = 8, b = 6



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



A = 22.90 °

C= 136.60 °

c = 17.66

B = 20° 30', a = 10, b = 9



B = 14.52 °

C= 22.48 °

c = 7.62

A = 143°, a = 12, b = 5


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


2 of 13 11/20/2017 01:09 PM

9. -Question Details LarTrig9 3.1.026.MI. [2548291]



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°




B = IMPOSSIBLE °

C= IMPOSSIBLE °

c = IMPOSSIBLE

A = 79°, a = 18, b = 19




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


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


3 of 13 11/20/2017 01:09 PM



B = 139°, a = 89, c = 37

1080.2


Area = ac sin(B) = (89)(37) sin(139°) ≈ 1080.212

12



33.7

C = 167°, a = 15, b = 20


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


C = 180° − 27° − 92° = 61°

h = sin(27°) ≈ 22.8 meters44sin(61°)


4 of 13 11/20/2017 01:09 PM


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


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°


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


5 of 13 11/20/2017 01:09 PM


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


6 of 13 11/20/2017 01:09 PM


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


7 of 13 11/20/2017 01:09 PM


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.


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.


Heron's Formula


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 °



A = 32.09 °

B = 20.74 °

C= 127.17 °


8 of 13 11/20/2017 01:09 PM



A= 42.85 °

B= 25.15 °

c= 10.91



A = 51°, b = 5, c = 15

a = 12.47

B = 18.15 °

C = 110.85 °


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 °


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


9 of 13 11/20/2017 01:09 PM


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°


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


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


10 of 13 11/20/2017 01:09 PM


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


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


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)


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


b2 = 2202 + 3802 − 2(220)(380)cos 105° b ≈ 485.9 meters


11 of 13 11/20/2017 01:09 PM

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

Which graded: Last

Before due date

Question Score

Assignment Score

Publish Essay Scores

Question Part Score

Mark

Add Practice Button

Help/Hints

Response

Save Work

After due date

Question Score

Assignment Score

Publish Essay Scores

Feedback Settings

Assignment Details


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 °


cos(θ) = ≈ -0.67018

θ ≈ 132.1°

1.92 + 32 − (4.5)2

2(1.9)(3)


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


12 of 13 11/20/2017 01:09 PM

Key

Question Part Score

Solution

Mark

Add Practice Button

Help/Hints

Response


13 of 13 11/20/2017 01:09 PM

Assignment Previewer ...smithies/TrigPostF17/TrigT3PracBSoln.pdf · The Law of Cosines can be used...

Documents

Transcript of Assignment Previewer ...smithies/TrigPostF17/TrigT3PracBSoln.pdf · The Law of Cosines can be used...