Law of Sines and Law of Cosines — a Deeper Look — Quiz
Question 5 • Precalculus
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 ?
Answer
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
Explanation
Expand the binomial using (b − x)² = b² − 2bx + x². Substituting that into c² = h² + (b − x)² gives c² = h² + b² − 2bx + x², which is choice B.
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