document.write( "Question 302049: a cellular phone tower services a 20 mile radius. A rest stop on the highway is 5 miles east and 12 miles north of the tower. If you continue driving due east, for how many miles will you be in range of the tower? \n" ); document.write( "
Algebra.Com's Answer #216785 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! a cellular phone tower services a 20 mile radius. \n" ); document.write( " A rest stop on the highway is 5 miles east and 12 miles north of the tower. \n" ); document.write( " If you continue driving due east, for how many miles will you be in range of the tower? \n" ); document.write( ": \n" ); document.write( "Let x = no. of miles east of the rest stop to max range (20 mi from center) \n" ); document.write( ": \n" ); document.write( "Draw a diagram. \n" ); document.write( "A circle, draw inside a rectangle 12n by 5w, lower left corner is at the center. \n" ); document.write( "The upper right corner is the rest stop, label the line from rest stop to a \n" ); document.write( "point on the circumference as x, from this same point a radius line to the center. \n" ); document.write( "This is a right triangle we can solve; a^2 + b^2 = c^2 \n" ); document.write( "a = 12 \n" ); document.write( "b = (x+5) \n" ); document.write( "c = 20 \n" ); document.write( ": \n" ); document.write( "12^2 + (x+5)^2 = 20^2 \n" ); document.write( "144 + x^2 + 10x + 25 = 400 \n" ); document.write( "x^2 + 10x + 144 + 25 - 400 = 0 \n" ); document.write( "A quadratic equation \n" ); document.write( "x^2 + 10x - 231 = 0 \n" ); document.write( "Factors to \n" ); document.write( "(x-11)(x+21) = 0 \n" ); document.write( "x = 11 mi east from rest stop to max range point \n" ); document.write( " |