Question
Download Solution PDFIf cos (A – B) = \(\frac{{\sqrt 3 }}{2}\), and cos (A + B) = 0, where A and B are positive acute angles and A \( \ge \) B, then the measures of A and B are:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
cos (A – B) = \(\frac{{\sqrt 3 }}{2}\)
cos (A + B) = 0
Concept used:
Values of angles of Cosine:
cos 0o = 1
cos 30o = \(\frac{{\sqrt 3 }}{2}\)
cos 45o = \(\frac{1}{\sqrt2}\)
cos 60o = \(\frac{1}{2}\)
cos 90o = 0
Calculations:
cos (A – B) = \(\frac{{\sqrt 3 }}{2}\) = cos 30o
A - B = 30o - - - - - - - -(1)
Cos (A + B) = 0 = cos 90o
A + B = 90o - - - - - - - -(2)
Adding equations 1 and 2, we get
A - B + A + B = 90o + 30o
2A = 120o
A = 60o
Put the value of A in eq 1,
A - B = 30o
60o - B = 30o
B = 30o
Thus, the measures of A and B are 60o and 30o respectively.
Last updated on Jul 22, 2025
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