Law of Cosines — Quiz Answers

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4

Which equation correctly uses the law of cosines to solve for the missing side length of △PQR ?

A
6 squared is equal to p squared plus 8 squared minus 2 p 8 cosine open paren 39 degrees close paren
B
p squared is equal to 6 squared plus 6 squared minus 2 6 6 cosine open paren 39 degrees close paren
C
8 squared is equal to 6 squared plus p squared minus 2 6 p cosine open paren 39 degrees close paren
D
p squared is equal to 6 squared plus 8 squared minus 2 6 8 cosine open paren 39 degrees close paren
5

What additional information did Abby know that is not shown in the diagram?

A
m angle cap k is equal to 37 degrees and n is equal to 31
B
m angle cap k is equal to 37 degrees and k is equal to 31
C
m angle cap n is equal to 37 degrees and n is equal to 31
D
m angle cap n is equal to 37 degrees and k is equal to 31
6

On which triangle can the law of cosines be used to find the length of an unknown side? Law of cosines: A squared is equal to b squared plus c squared minus 2 b c cosine cap A

A
Image with description Triangle Q R S is shown. The measure of the angles R S Q and R Q S are 57 and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as q, 12, and s.
B
Image with description Triangle Q R S is shown. The measure of the angles R S Q and R Q S are 57 and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as 7, b, and s.
C
Image with description Triangle Q R S is shown. The measure of the angle R S Q is 57 degrees. The length of the sides R S, S Q, and Q R are labeled as 7, 12, and s.
D
Image with description Triangle Q R S is shown. The measure of the angles Q R S, R S Q, and S Q R are 87, 57, and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as q, 12, and s.
7

On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: A squared is equal to b squared plus c squared minus 2 b c cosine cap A

A
Image with description Triangle X W Y is shown. The measure of the angle X Y W is 76 degrees. The length of the sides X Y, Y W, and W X are labeled as 5, 10, and y.
B
Image with description X Y Z is a triangle, right angled at Y. The length of the sides X Y, Y W, and W X are labeled as a, 9, and y.
C
Image with description Triangle X W Y is shown. The length of the sides X Y, Y W, and W X are 8, 16, and 10.
D
Image with description Triangle W X Y is shown. The length of the sides X W and X Y are congruent. The length of the side W Y is 7.
8

To the nearest whole degree, what is the measure of angle cap z ?

A
41 degrees
B
57 degrees
C
51 degrees
D
47 degrees
9

To the nearest whole degree, what is the measure of angle cap q ?

A
44 degrees
B
49 degrees
C
59 degrees
D
54 degrees
10

What is the measure of angle cap c to the nearest whole degree?

A
85 degrees
B
70 degrees
C
80 degrees
D
77 degrees

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