Question 829545
The legs of a right triangle are the 2 sides
that are 90 degrees to each other.
The 3rd side is the hypotenuse.
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Let {{{ a }}} = one of the legs
Let {{{ b }}} = the other leg
Let {{{ c }}} = the hypotenuse
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The pythagorean theorem says:
{{{ a^2 + b^2 = c^2 }}}
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For your problem, you can say {{{ a = 3 }}} ft
The length of the ladder is the hypotenuse,
so {{{ c = 12 }}} ft
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The distance from the ground to where the ladder
touches the wall is {{{ b }}}, so
{{{ 3^2 + b^2 = 12^2 }}}
{{{ 9 + b^2 = 144 }}}
{{{ b^2 = 135 }}}
{{{ b = sqrt(135) }}}
{{{ b = 11.619 }}} ft
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check:
{{{ a^2 + b^2 = c^2 }}}
{{{ a3^2 + 11.619^2 = 12^2 }}}
{{{ 9 + 135.001 = 144 }}}
{{{ 144.001 = 144 }}}
close enough
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Your other problem is
{{{ 4^2 + 5^2 = c^2 }}}
{{{ 16 + 25 = c^2 }}}
{{{ c^2 = 41 }}}
{{{ c = sqrt(41) }}}
{{{ c = 6.403 }}} meters is the
diagonal distance