If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ABC is

• 10.5 bcz from the given data it is right angled triangle (satisfies pithogorous theoram ) now if angle bisector of 'a' will splits line BC 15 in to two equal parts... now apply pythogorus theoram here again between newly formed triangle AB,BC',C'A (c' is angle bisector of A) then we will get 10.5
  
• 11 years agoHelpfull: Yes(19) No(10)
• (120 root2)/23
  
• 10 years agoHelpfull: Yes(5) No(0)
• Given triangle is Right angled at B
  Length of Angle bisector of angle ∟ABC is
  (2*c*a)*cos(B/2)/(c+a)=(2*8*15)*cos(45)/(8+15)=(2*120/23)*(1/√2)=(120*√2)/23
• 9 years agoHelpfull: Yes(4) No(0)
• length of angle bisector in rt triangle is (2ca cos( b/2)) / c+a .. it will not bisect the hypotenuse. ans (120 root 2 )/ 3
• 11 years agoHelpfull: Yes(1) No(0)
• as the given sides are of pythagoras triplets (8,15,17)..
  sotriangle ABC is a right angled triangle, right angled at B..
  
  as angle bisector of ABC will bisect the angle only... so draw a line from B to AC (say D)and it makes..
  
  NOW the angle anglDBC=ANGLDBA=45
  
  now a property of angle bisector,
  AB/BC=AD/CD
  8/15=AD/CD
  AS AC IS 17
  AD=(8/23)*17= 5.9
  NOW WE KNOW TWO SIDES OF TRIANGLE ABD AND ONE ANGLE IS 45
  WE CAN USE COSINE RULE AND WE WILL GET BD
• 9 years agoHelpfull: Yes(1) No(1)
• 8,15 and 17 are sides of a right angle triangle and ABC is a right angle.the angle bisector of abc will be perpendicular(say X) on side AC.
  now,
  1/2*8*15 = 1/2*X*17(area of triangle)
  after solving this we get X=7.06
• 9 years agoHelpfull: Yes(0) No(2)
• a=15,b=17,c=8
  by cosine rule:
  b^2=a^2+c^2-2ac*cosB
  289=225+64-2*8*15*cosB
  cosB=0
  B=90
  
  SO,eventualy the angle bisector of angle ABC will bisect AC
  and the length of angle bisector will be=ac/a+b+c=(15*8)/(15+8+17)=3cm
  So ...a/c to me correct answer is 3cm!
  
• 9 years agoHelpfull: Yes(0) No(1)
• (ANS- 6.3) Here AB= 8(base), BC= 15(perpendicular) and AC= 17(hypotenuse), now angle bisector of ABC bisects AC into two parts (8.5 each). In New right angled triangle ABC', AB= 8, AC'= 8.5 and BC'= ?
  (apply pythagorous theorm)
• 8 years agoHelpfull: Yes(0) No(0)
• Its a rt. angled triangle from the (8 15 17) triplet. Now applying Apollonius' theorem 8^2+15^2=2(x^2+8.5^2) {x=angle bisector and 8.5 is half of side 17}
• 8 years agoHelpfull: Yes(0) No(1)