AnswersIC Pre-Cal - DeeringLaw of Sines

Law of Cosines Answers

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Bethany used the steps below in an attempt to solve for angle B in triangle ABC. Where is Bethany’s error?

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A
Bethany made one side of the equation equal to the square of the incorrect side when solving for B.
B
Bethany took the square root of each squared term before isolating cosB and solving for B.
C
Bethany used cosine instead of inverse cosine when finding B.
D
Bethany neglected to multiply the expression involving the cosine by 2.
2
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What is the approximate measure of angle T in the triangle below?

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A
79°
B
84°
C
96°
D
101°
3

Which equation can be used to solve for x in the triangle below?

Question illustration
A
x squared equal to 4 point 7 squared plus 4 point 0 squared + 2 (4.7) (4.0) cosine 41 degree.
Option A
B
x equal to 4 point 7 plus 4 point 0 plus 2 (4.7) (4.0) cosine 41 degree.
Option B
C
x squared equal to 4 point 7 squared plus 4 point 0 squared - 2 (4.7) (4.0) cosine 41 degree.
Option C
D
x equal to 4 point 7 plus 4 point 0 minus 2 (4.7) (4.0) cosine 41 degree.
Option D
4

What is the approximate length of the third side of the triangle below?

Question illustration
A
22.2 mm
B
25.8 mm
C
35.5 mm
D
46.1 mm
5

Which equation can be used to solve for angle N in the triangle below?

Question illustration
A
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared minus 2 (3.6) (4.3) cosine N.
Option A
B
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared plus 2 (3.6) (4.3) cosine N.
Option B
C
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared minus (3.6) (4.3) cosine N.
Option C
D
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared plus (3.6) (4.3) cosine N.
Option D
6

In order to make a precise cut from point Q to point S using a saw, Alfonso needs to know the angle measure for the angle whose vertex is S. Based on the diagram below, which equation could Alfonso use to determine the measure of angle S?

Question illustration
A
9 = 10 + 11 - 2(10)(11)cosS
Option A
B
10 = 9 + 11 - 2(9)(11)cosS
Option B
C
9 = 10 + 11 + 2(10)(11)cosS
Option C
D
10 = 9 + 11 + 2(9)(11)cosS
Option D
7

Based on the diagram below, which expression can be used to determine the distance between Seattle, WA, and San Francisco, CA? [Not drawn to scale]

Question illustration
A
StartRoot 1858 squared plus 1737 squared minus 2 (1858) (1737) cosine 21 point 4 EndRoot
Option A
B
StartRoot 1858 squared plus 1737 squared plus 2 (1858) (1737) cosine 21 point 4 EndRoot
Option B
C
1858 plus 1737 minus 2 (1858) (1737) cosine 21 point 4
Option C
D
1858 plus 1737 plus 2 (1858) (1737) cosine 21.4
Option D
8

An archer fires two arrows into a raised target, as represented in the diagram below. About how much greater of an angle did the archer need to use in order for the second arrow to land 7 feet higher than the first arrow?

Question illustration
A
1.0°
B
1.6°
C
6.0°
D
8.7°
9

A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?

A
103.1 mi.
B
174.7 mi.
C
214.7 mi.
D
226.5 mi.
10

In triangle RST, RS = 6 cm, ST = 7 cm, and RT = 8 cm. What is the approximate measure of the largest angle in the triangle?

A
60.0°
B
63.0°
C
75.5°
D
86.6°

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