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Answer:
JK = 6.86
Step-by-step explanation:
The parameters given are;
LJ = 14
JM = 48
LM = 50
[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]
[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]
∠JML = 16.26°
Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.
From the angle bisector theorem, we have;
LM/JM = LK/JK
50/48 = LK/JK................(1)
LK + KJ = 14.....................(2)
From equation (1), we have;
LK = 25/24×JK
25/24×KJ + JK = 14
JK×(25/24 + 1) = 14
JK × 49/24 = 14
JK = 14×24/49 = 48/7. = 6.86.
JK = 6.86
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Rewritten by : Barada
The calculation of JK cannot be completed due to inadequate information in the question about the triangle's specifics, such as point K's location and whether it's a right triangle.
The question requests the calculation for the length of segment JK, given a triangle with lengths of the other sides provided (LJ = 14, JM = 48, and LM = 50). Generally, when dealing with lengths within a triangle, the Pythagorean theorem is applied. However, in this scenario, the segment JK is not specifically defined in context. We require more information about this triangle such as point K's location, whether it's a right triangle, or the angles at each point. Essentially, we can't figure out JK's length without further data.
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