document.write( "Question 1197859: From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. From a point B that is 46 feet further from the tree, the angle of elevation is 22 degrees. Which of the following is the height of the tree.
\n" ); document.write( "A. 34.1 feet
\n" ); document.write( "B. 35.8 feet
\n" ); document.write( "C. 36.7 feet
\n" ); document.write( "D. 37.2 feet
\n" ); document.write( "E. 38.5 feet \n" ); document.write( "
Algebra.Com's Answer #831558 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. From a point B that is 46 feet further from the tree, the angle of elevation is 22 degrees. Which of the following is the height of the tree.
\n" ); document.write( "A. 34.1 feet
\n" ); document.write( "B. 35.8 feet
\n" ); document.write( "C. 36.7 feet
\n" ); document.write( "D. 37.2 feet
\n" ); document.write( "E. 38.5 feet
\n" ); document.write( "
.\r\n" );
document.write( "As ∡CAD = 38o, ∡CAB = 180 - 38 = 142o\r\n" );
document.write( "In ΔABC, ∡BCA = 180 - (142 + 22), or 38 - 22 = 16o\r\n" );
document.write( "Use Law of Sines to find AC, as follows:  \r\n" );
document.write( "                                      AC * sin 16o = 46 * sin 22o ------ Cross-multiplying\r\n" );
document.write( "                                               \"matrix%281%2C3%2C+AC%2C+%22=%22%2C+%2846+%2A+sin+%2822%5Eo%29%29%2Fsin+%2816%5Eo%29%29\"\r\n" );
document.write( "                                               Continue solving for AC\r\n" );
document.write( "\r\n" );
document.write( "                                 We then have: \"matrix%281%2C5%2C+sin+%28CAD%29%2C+%22=%22%2C+O%2FH%2C+%22=%22%2C+CD%2FAC%29\"\r\n" );
document.write( "                                              \"matrix%281%2C3%2C+sin+%2838%5Eo%29%2C+%22=%22%2C+CD%2FAC%29\"\r\n" );
document.write( "Since AC is already known (from above), you need to CONTINUE onward and solve for CD, the height of the tree. \r\n" );
document.write( "\r\n" );
document.write( "When done, you should get a height of approximately 38.49115544, which when rounded to 1 decimal place, is about 38.5'(CHOICE E.).
\n" ); document.write( "
\n" );