In triangle ABC, angle C has a measure of 60 degrees. Point D lies on side AC so that BD bisects angle B and BD = 1. Similarly, point E lies on side BC so that AE bisects angle A and AE = 2.
Find the area of triangle ABC.
It is easy to verify that if B is a right angle,
then |AE| = 2|BD|.
Applying the law of sines to triangle BCD gives,
|BC| |BC| |BD| 1
--------- = ---------- = ---------- = ---------
sin(75) sin(BDC) sin(BCD) sin(60)
or
sin(75)
|BC| = ---------
sin(60)
Therefore,
Area(ABC) = (1/2)|AB||BC| = (1/2)|BC|^2*tan(60)
sin(75)^2
= ----------- ~= 1.07735
sin(60)
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Posted by Bractals
on 2008-02-11 13:41:41 |
Solution
