document.write( "Question 1024269: Construct a triangle ABC if perimeter is 11.5 base angle is angle B=60°and angle C=50°. \n" ); document.write( "

Algebra.Com's Answer #639706 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Construct a triangle ABC if perimeter is 11.5 base angle is angle B=60°and angle C=50°.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1. Although it was not declared explicitly in the condition, it is assumed implicitly \r\n" );
document.write( "   that the angles B and C are given as the instances at the plane.\r\n" );
document.write( "   It doesn't matter that they are 60° and 50°. I mean: their numerical values do not matter.\r\n" );
document.write( "   What really does matter is that these angles are given as instances, so you do not need worry on construction the angle of 50°.\r\n" );
document.write( "\r\n" );
document.write( "   (So, actually the condition in this post is not precisely correct.\r\n" );
document.write( "    The correct formulation should be like this: \r\n" );
document.write( "        \"Construct a triangle ABC with the given perimeter and two given angles B and C.\")\r\n" );
document.write( "    How it is really formulated in the post is making a fog . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2. Having given these two angles B and C, construct an arbitrary triangle with these two angles B and C. \r\n" );
document.write( "   I mean, construct a triangle with an arbitrary side length concluded between these two angles.\r\n" );
document.write( "\r\n" );
document.write( "   It is obvious how to do it, and since it is obvious, I will not explain it more.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3. Now, the triangle you constructed is similar to the required triangle.\r\n" );
document.write( "   All you need to do is to adjust the triangle you just constructed, in a way to get \r\n" );
document.write( "   the perimeter of the adjusted triangle 11.5 cm  (11.5 units . . . ).\r\n" );
document.write( "   It is clear that the major task is to adjust the side BC of the constructed triangle. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4. The key procedure for it is described in the lesson \r\n" );
document.write( "       HOW TO construct the segment whose length is an unknown term of a proportion \r\n" );
document.write( "   in this site.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "5. On one side of the given angle B mark the segment whose length is the perimeter of the constructed triangle.\r\n" );
document.write( "   Mark its endpoint as P.\r\n" );
document.write( "   On the same side of the given angle attach the segment whose length is the corresponding side BC of the constructed triangle. \r\n" );
document.write( "   Mark the endpoint as Q.\r\n" );
document.write( "\r\n" );
document.write( "   On the other side of the given angle B mark the segment whose length is the GIVEN perimeter. \r\n" );
document.write( "   Mark its endpoint as R.\r\n" );
document.write( "\r\n" );
document.write( "   Connect P and R.\r\n" );
document.write( "\r\n" );
document.write( "   Next draw a straight line from Q parallel to PR.\r\n" );
document.write( "   Mark S its intersection with BR.\r\n" );
document.write( "\r\n" );
document.write( "   Now RS is the actual side \"newBC\" of your adjusted triangle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "6. Re-construct the triangle with the side \"newBC\" and the angles B and C.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "7. The problem is solved.\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );