Question

I 23 12 N L 12 23 O K M 18 18

Answer 1

Answer: $\sqrt{407}$

Step-by-step explanation:

In this triangle, we know that $IJ=46, IK=24, JK=36$.

So, using the Law of Cosines in triangle IJK,

$36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}$

Using the Law of Cosines in the triangle LIK,

$(KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}$