AnswersPrecalculusLaw of Sines and Law of Cosines — a Deeper Look

Law of Sines and Law of Cosines — a Deeper Look — Quiz Answers

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1
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Which equation here is a true statement about triangle ABC ?

A
sine cap A is equal to h over b
B
sine cap c is equal to h over A
C
sine cap c is equal to A over h
D
sine cap c is equal to h over b
2
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Which equation represents the Law of Sines for triangle ABC ?

A
c sine cap c is equal to b sine cap b
B
sine cap A over b is equal to sine cap b over A
C
b sine cap b is equal to A sine cap A
D
sine cap A over A is equal to sine cap b over b
3

Solve the Law of cosines: c squared is equal to A squared plus b squared minus 2 A b cosine cap c for cosine cap c .

A
cosine cap c is equal to the fraction with numerator negative c squared plus A squared plus b squared and denominator negative 2 A b
B
cosine cap c is equal to the fraction with numerator A squared plus b squared minus c squared and denominator 2 A b
C
cosine cap c is equal to the fraction with numerator c squared minus A squared minus b squared and denominator 2 A b
D
cosine cap c is equal to the fraction with numerator A squared plus b squared plus c squared and denominator negative 2 A b
5

In the proof of the Law of Cosines, the equation c squared is equal to h squared plus open paren b minus x close paren squared was created using the Pythagorean theorem. Which equation is a result of expanding (b−x)^2 ?

A
c squared is equal to h squared plus b squared plus x squared
B
c squared is equal to h squared plus b squared minus 2 b x plus x squared
C
c squared is equal to h squared plus b squared minus 2 b x minus x squared
D
c squared is equal to h squared plus b squared minus x squared
6

Which equation given is a true statement about triangle ABC ?

A
h is equal to A cosine cap c
B
cosine cap c is equal to h over A
C
cosine cap c is equal to h over b
D
x is equal to b minus A cosine cap c
8

Sophia wants to solve for the side length of b Which equation could Sophia use to solve for the side length of b , given the other two side lengths and the measure of their included angle?

A
b squared is equal to A squared plus c squared minus 2 A b cosine cap c
B
b squared is equal to A squared plus c squared minus 2 A c cosine cap A
C
b squared is equal to A squared plus c squared minus 2 A c cosine cap c
D
b squared is equal to A squared plus c squared minus 2 A c cosine cap b
9

In triangle ABC shown, sine cap c is equal to h over A and sine cap A is equal to h over c Which of the following combines the two sine ratios into one equation?

A
sine cap c over A is equal to sine cap A over c
B
h over sine cap c is equal to h over sine cap A
C
A sine cap c is equal to c sine cap A
D
h sine cap c is equal to h sine cap A
10

Which equation is a true statement about triangle CBD shown?

A
h squared is equal to A squared plus x squared
B
h squared is equal to A squared plus b squared
C
h squared is equal to A squared minus b squared
D
h squared is equal to A squared minus x squared

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