Triangle with median and altitude

  • #1
utkarshakash
Gold Member
855
13

Homework Statement


In triangle ABC with A as obtuse angle, AD and AE are median and altitude respectively. If BAD = DAE=EAC, then sin^3(A/3)cos(A/3) equals

Homework Equations


The Attempt at a Solution



CE = a/2. Let DE = x. Then BD = a/2 - x.
Let AE = p, AD = q.

For ΔADB

[itex]\cos \frac{A}{3} = \dfrac{q^2+c^2-(a/2 -x)^2}{2cq}[/itex]

I can also write cos A/3 for other two triangles using the same approach but I don't know which one to use in the final expression. Also it will contain p and q which is unknown. I have no idea what sin(A/3) would be. This seems really complicated. :cry:
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
hi utkarshakash! :smile:
For ΔADB

[itex]\cos \frac{A}{3} = \dfrac{q^2+c^2-(a/2 -x)^2}{2cq}[/itex]

why use such an awkward triangle? :redface:

there are three right-angled triangles …

use them! :wink:
 
  • #3
utkarshakash
Gold Member
855
13
hi utkarshakash! :smile:


why use such an awkward triangle? :redface:

there are three right-angled triangles …

use them! :wink:

How could I miss them?:tongue2: Thanks a lot.
 

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