In a triangle ABC, D is the midpoint of BC. Join AD. Angle ADB = 45 degree and angle ACB = 30 degree. Find angle ABC.
WOLOG let |BD| = |DC| = 1.
|AD| |DC| 1
--------- = --------- = ---------
sin(30) sin(15) sin(15)
or
|AD| = 2 cos(15)
|AD| |BD|
-------- = ------------
sin(?) sin(135-?)
or
2 cos(15) 1
----------- = ------------
sin(?) sin(135-?)
or
Angle ABC = ? = 105 degrees
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Posted by Bractals
on 2006-02-25 11:18:25 |
Solution
