SOLUTION: The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0� < A

SOLUTION: The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0� < A < 90�.

Question 1113961: The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0� < A < 90�.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0� < A < 90�.
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Equation::
(1/3)/[(1/24)sin(A)] = [tan(A)/(1/3)]
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Cross-multiply
(1/24)sin(A)*tan(A) = 1/9
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[sin^2(A)/cos(A)] = (1/9)/(1/24)
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(1-cos^2(A))/cos(A) = (8/3)
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3-3cos^2(A)- 8cos(A) = 0
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3cos^2(A) + 8cos(A) -3 = 0
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cos(A) = [-8+-sqrt(64-4*3*-3)]/(2*3)
Positive answer = 2/(2*3) = 1/3
Negative answer = -18/(6) = -3 (not acceptable for cosine value)
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Cheers,
Stan H.
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