document.write( "Question 1137442: How can I solve this exercise?
\n" ); document.write( "Suppose A=30∘ and b=10. Then there is one value of a that is less than b and for which there is a unique triangle with the data A, a, and b. That value of a is? \n" ); document.write( "

Algebra.Com's Answer #755311 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Draw a sketch with the 30 degree angle A at the left, one ray of the angle horizontal, and ray b upwards to the right at a 30 degree angle.

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\n" ); document.write( "If ABC is a right triangle, then a/b = sin(30) = 1/2, so a=5.

\n" ); document.write( "If a is less than 5, no triangle is formed, because a is not long enough to reach from C to ray AB.

\n" ); document.write( "If a is greater than 5, then two different triangles can be formed -- one with angle B acute and another with angle B obtuse.

\n" ); document.write( "So the only value of a less than b for which there is a unique triangle with measurements A, a, and b is a=5. \n" ); document.write( "

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