document.write( "Question 823989: Hi,
\n" ); document.write( "I know that the area of a triangle is 1/2 bh but that is not one of the answers.
\n" ); document.write( "How can I find the area in this triangle?\r
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Algebra.Com's Answer #495992 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Rule:\r
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\n" ); document.write( "\n" ); document.write( "Area of Triangle = (Base)*(Height)/2\r
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\n" ); document.write( "\n" ); document.write( "Note: the base and height are ALWAYS perpendicular segments\r
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\n" ); document.write( "\n" ); document.write( "Since h is the height (given and fixed), this forces us to choose b as the base since b is perpendicular to h\r
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\n" ); document.write( "\n" ); document.write( "So....\r
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\n" ); document.write( "\n" ); document.write( "Area of Triangle = (Base)*(Height)/2\r
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\n" ); document.write( "\n" ); document.write( "A = b*h/2\r
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\n" ); document.write( "\n" ); document.write( "-------------------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( "Now focus on the smaller triangle on the left (with hypotenuse 'a' and leg 'h')\r
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\n" ); document.write( "\n" ); document.write( "sin(angle) = opposite/hypotenuse\r
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\n" ); document.write( "\n" ); document.write( "sin(theta) = h/a\r
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\n" ); document.write( "\n" ); document.write( "a*sin(theta) = h\r
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\n" ); document.write( "\n" ); document.write( "h = a*sin(theta)\r
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\n" ); document.write( "\n" ); document.write( "Now go back to the area of a triangle equation and plug h = a*sin(theta) in\r
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\n" ); document.write( "\n" ); document.write( "A = b*h/2\r
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\n" ); document.write( "\n" ); document.write( "A = (1/2)*b*h\r
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\n" ); document.write( "\n" ); document.write( "A = (1/2)*b*(a*sin(theta))\r
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\n" ); document.write( "\n" ); document.write( "A = (1/2)ab*sin(theta)\r
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\n" ); document.write( "\n" ); document.write( "So the answer is choice D
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