document.write( "Question 1070440: A ladder placed on a flat horizontal surface rests against a vertical wall with an angle of elevation of 60°. The foot of the ladder is 2 m from the best of the wall. Find the height of the point where the ladder touches the wall \n" ); document.write( "

Algebra.Com's Answer #685622 by KMST(5328) $\"\"$ $\"About$

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The ladder, the vertical wall, and the horizontal ground
\n" ); document.write( "form a right triangle.
\n" ); document.write( "With $\"h\"$ = height where the ladder touches the wall
\n" ); document.write( " $\"L\"$ = length of the ladder and
\n" ); document.write( " $\"x\"$ = distance from the bottom of the ladder to the wall,
\n" ); document.write( "the trigonometric ratios that apply are
\n" ); document.write( " $\"sin%2860%5Eo%29=h%2FL\"$ ,
\n" ); document.write( " $\"cos%2860%5Eo%29=x%2FL\"$ , and
\n" ); document.write( " $\"tan%2860%5Eo%29=h%2Fx\"$ .
\n" ); document.write( "You want to find $\"h\"$ .
\n" ); document.write( "If you had been given $\"L\"$ , you would use $\"sin%2860%5Eo%29=sqrt%283%29%2F2\"$ ,
\n" ); document.write( "and in many problems you are given the length of the ladder.
\n" ); document.write( "However, this problem gives you $\"x\"$ ,
\n" ); document.write( "so you need to use $\"tan%2860%5Eo%29=sqrt%283%29=about1.732\"$
\n" ); document.write( " $\"1.732=h%2F%222+m%22\"$ ---> $\"h=%28about1.732%29%2A2m=about3.46m\"$ . \n" ); document.write( "

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