Find the length of one side of a triangle given two other sides and the length of the angle bisectorFor an arbitrary triangle ABC.If given the length of side A B = 15 and A C = 12 and the length of the angle bisector that connects angle A to side B C = 10. What is the length of BC.

Question

Find the length of one side of a triangle given two other sides and the length of the angle bisectorFor an arbitrary triangle ABC.If given the length of side   A  B  =  15 and   A  C  =  12 and the length of the angle bisector that connects angle A to side   B  C  =  10. What is the length of BC.

eyiliweyouc · Accepted Answer

Step 1using angle bisector theorem:BC is split in the ratio 4k to 5k.Step 2From the length of the angle bisector formula:  180  −  20      k    2    =      10    2      ⟹    k  =  2  B  C  =  18

Quessyrutty6w · Accepted Answer

Step 1I&#039;m going to solve this using Trigonometry. Let   △  A  B  C have sides   A  B  =  c     B  C  =  a and   C  A  =  b then,   C  o  s  A  =  2  C  o      s    2    (  A      /    2  )  −  1Step 2By cosine rule   C  o  s  A  =                    b        2            +              c        2            −              a        2                    2      b      c      And the length of angle bisector of Angle A is given by,   A  D  =            2      b      c      C      o      s      (      A              /            2      )              b      +      c      Substituting   A  D  =  10  ,  A  B  =  15  ,  A  C  =  12 we get   C  o  s  (  A      /    2  )  =  3      /    4. And then   C  o  s  A  =  1      /    8. And finally use cosine rule to get   B  C  =  18

If given the length of side AB=15 and AC=12 and the length of the angle bisector that connects angle A to side BC=10. What is the length of BC.

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