Question

If ABC is a triangle with AB=20,BC=22 and CA=24. Let D lie on BC such that AD is the angle bisector of ∠BAC.

Answer 1

find \[AB^2\]

Answer 2

is an angle bisector also a side bisector

Answer 3

ie in a triangle

Answer 4

@satellite73 @shubhamsrg @phi

Answer 5

in general, no the angle bisector does not bisect the opposite side
(It does if you had an isosceles triangle)

Answer 6

what are you trying to find ?

Answer 7

AB^2

Answer 8

Does AB mean length of side AB ? Because they give you that, and you just square it.

Answer 9

sorry AD^2

Answer 10

This looks painful

One way is to use the law of cosines and find all three angles A, B, and C of the triangle.

Can you do that ?

Answer 11

once you have the 3 angles we can take the next step.

Answer 12

wat i did so far
\[x^2=AD^2+24^2-2AB24\cos \theta\]
\[(22-x)^2=AD^2+20^2-2AD20\cos \theta\]
\[22^2=24^2+20^2-2(24)(20)\cos 2\theta\]