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maksim [4K]
2 years ago
15

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

Mathematics
1 answer:
soldi70 [24.7K]2 years ago
8 0

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}

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