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 Angle Bisectors (Posted on 2008-02-11)
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.

 See The Solution Submitted by Dennis Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 1 of 5
`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) `
` `

 Posted by Bractals on 2008-02-11 13:41:41
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