document.write( "Question 1202951: Evaluate the expression:
\n" ); document.write( "sin^(-1)⁡(2/5)+sin^(-1)(√21/5) \n" ); document.write( "

Algebra.Com's Answer #838159 by Theo(13342) $\"\"$ $\"About$

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sin^(-1)(2/5) = 23.57017848 degrees.
\n" ); document.write( "sin^*(-1)(sqrt(21)/5) = 66.42182152 degrees.
\n" ); document.write( "23.57017848 degrees + 66.42182152 degrees = 90 degrees.
\n" ); document.write( "that's your solution.
\n" ); document.write( "the angles are complementary.
\n" ); document.write( "if you put them in the same right triangle, your triangle would have:
\n" ); document.write( "angle A = 23.57017847
\n" ); document.write( "angle B = 66.42182152
\n" ); document.write( "angle C = 90
\n" ); document.write( "given that sin(23.57017848) = 2/5, you have side opposite angle A = 2 and side opposite angle C = 5
\n" ); document.write( "given that sin(66.42182152) = sqrt(21) / 5, you have side opposite angle B = sqrt(21) and side opposite angle C = 5.
\n" ); document.write( "since side opposite angle A squared plus side opposite angle B squared = side opposite angle C squared, you get (2/5)^2 + (sqrt(21)/5)^2 = 5^2.
\n" ); document.write( "this becomes 4/25 + 21/25 = 25 which is true, confirming the value of the angles is correct.\r
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