AnswersNC-Math 4 CRLaw of Cosines

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?

Question illustration
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 length of the missing side in the triangle below?

Question illustration
A
13.9 mi.
B
19.0 mi.
C
21.3 mi.
D
25.4 mi.
3

A ship heads due north for x miles, then turns 25° east of north and travels for another y miles. Which expression represents the distance the ship is from the original starting point?

A
x plus y minus StartRoot 2 xy cosine 155 degree EndRoot.
Option A
B
StartRoot x squared plus y squared minus 2 xy cosine 155 degree EndRoot.
Option B
C
x plus y minus StartRoot 2 xy cosine 25 degree EndRoot.
Option C
D
StartRoot x squared minus y squared minus 2 xy cosine 25 degree EndRoot.
Option D
4

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
5

A 15-foot flagpole leans slightly, such that it makes an 80° angle with the ground. The shadow of the flagpole is 10 feet long when the sun has an unknown angle of elevation. How could the angle of elevation of the sun, x, be determined?

Question illustration
A
by determining the length of TV using , and then determining the value of x using
Option A
B
by determining the value of x using
Option B
C
by determining the length of TV using , and then determining the value of x using
Option C
D
by determining the value of x using
Option D
6

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
7

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
8

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
9

In triangle MNO, MN = 20 units, NO = 15 units, and MO = 18 units. What is the approximate difference between the largest and smallest angle measures?

A
2°
B
5°
C
14°
D
28°
10

Four students drew four different triangles in math class. Which triangle can be solved using only the law of cosines?

Question illustration
A
Anna’s triangle
B
Yuna’s triangle
C
Carly’s triangle
D
Saki’s triangle

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