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Equal angles within a right triangle (Posted on 2020-01-08) Difficulty: 2 of 5
Given: △EAD with ∠A=90. B and C on segment AD with AB=1, BC=2, CD=3. ∠ADE≅∠BEC.

Find AE

No Solution Yet Submitted by Jer    
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Solution Using some trig | Comment 1 of 2
Let x = length of  AE
Let t = the two angles ∠ADE and ∠BEC
Let s = ∠AEB

tan(t) = x/6
tan(s) = 1/x
tan(s+t) = 3/x
tan(s+t) = [tan(s) + tan(t)] / [1 - tan(s) * tan(t)]

3/x = [1/x + x/6] / [1 - 1/x * x/6]
3/x = [1/x + x/6] / [1 - 1/6]
(3/x)*(5/6) = (1/x + x/6)
5/2 = (1 + x^2/6)
15 = 6 + x^2
x^2 = 9
x = 3

So the length of AE is 3

  Posted by Larry on 2020-01-09 10:46:27
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