Question

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

Answer 1

Answer:
`√(407)`

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)=(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((349)/(552) \right)\\\\(KL)^2 = 407\\\\KL=√(407)`