document.write( "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°. \n" ); document.write( "
Algebra.Com's Answer #728982 by stanbon(75887)\"\" \"About 
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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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\n" ); document.write( "Equation::
\n" ); document.write( "(1/3)/[(1/24)sin(A)] = [tan(A)/(1/3)]
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\n" ); document.write( "Cross-multiply
\n" ); document.write( "(1/24)sin(A)*tan(A) = 1/9
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\n" ); document.write( "[sin^2(A)/cos(A)] = (1/9)/(1/24)
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\n" ); document.write( "(1-cos^2(A))/cos(A) = (8/3)
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\n" ); document.write( "3-3cos^2(A)- 8cos(A) = 0
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\n" ); document.write( "3cos^2(A) + 8cos(A) -3 = 0
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\n" ); document.write( "cos(A) = [-8+-sqrt(64-4*3*-3)]/(2*3)
\n" ); document.write( "Positive answer = 2/(2*3) = 1/3
\n" ); document.write( "Negative answer = -18/(6) = -3 (not acceptable for cosine value)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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