Question 1159929


{{{JK=2}}}
{{{LK=9}}}
{{{MK }}}perpendicular to {{{JL}}}

{{{MK}}}=?

since {{{MK}}}  and {{{LK}}} are legs of right triangle {{{LKM}}},  and {{{ML}}} is hypotenuse


first we need to calculate the length of {{{ML}}} using  tangent secant rule

{{{(ML)^2=LK*LJ}}}................since {{{LJ=LK+JK=9+2=11}}}

{{{(ML)^2=9*11}}}

{{{(ML)^2=99}}}


then, use Pythagorean theorem to find {{{MK}}} :

{{{(MK)^2= (ML)^2-(LK)^2}}}

{{{(MK)^2= 99-81}}}

{{{(MK)^2= 18}}}

{{{MK= sqrt(18)}}}

{{{MK= sqrt(9*2)}}}

{{{MK=3sqrt(2)}}}