document.write( "Question 370114: I have a right triangle, triangle ABC. Angle A is 70 degrees, angle B is 20 degrees and obviously, Angle C is 90. The length of side AB, or the opposite side is 183 miles. The length of side CB, or the base, is 172. What is the third side's length? \n" ); document.write( "

Algebra.Com's Answer #263822 by jsmallt9(3758) $\"\"$ $\"About$

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If C is the right angle then AB is the hypotenuse. With two sides of a right triangle we can use the Pythagorean Theorem to find the third side:
\n" ); document.write( " $\"%28183%29%5E2+=+%28172%29%5E2+%2B+%28AC%29%5E2\"$
\n" ); document.write( "Simplifying we get:
\n" ); document.write( " $\"33489+=+29584+%2B+%28AC%29%5E2\"$
\n" ); document.write( "Subtracting 29584 from each side we get:
\n" ); document.write( " $\"3905+=+%28AC%29%5E2\"$
\n" ); document.write( "Finding the square root of each side (and discarding the negative square root because sides of triangles cannot be negative):
\n" ); document.write( " $\"sqrt%283905%29+=+sqrt%28%28AC%29%5E2%29\"$
\n" ); document.write( " $\"sqrt%283905%29+=+AC\"$
\n" ); document.write( "which is the exact answer. Use your calculator on the square root to find a decimal approximation.
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