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# Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a

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Math Expert
Joined: 02 Sep 2009
Posts: 56277
Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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02 Sep 2018, 23:12
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74% (01:41) correct 26% (01:49) wrong based on 53 sessions

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Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° and angle CBD is 45°, how much longer is AB than DC?

(1) The length of BC is 12.
(2) The length of CA is 6.

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Posts: 7764
Re: Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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02 Sep 2018, 23:55
1
Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° and angle CBD is 45°, how much longer is AB than DC?

triangle ACB is 30-60-90 so sides are $$1:\sqrt{3}:2=AC:AB:BC$$ and triangle DCB is 45-45-90 so sides are $$1:1:\sqrt{2}=CD:DB:BC$$
Thus all 6 lines are interconnected. Knowing one side can give us all length and thus AB-DC also

(1) The length of BC is 12.
BC=12
we can know all sides
suff

(2) The length of CA is 6.
AC=6
we can know all sides
suff

D
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Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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03 Sep 2018, 00:40

Triangle CBD us isoceles.

And hence with one side bc we can find bd or CD - statement 1

With AC and BC we can find AB.

Hence we can find the difference.

So both statement together can find the result

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Re: Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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27 Feb 2019, 17:13
Both are special triangles (30-60-90 and 45-45-90). Since they share a hypotenuse knowing any concrete value gives us all the rest through the ratios x:x√3:2x and a:a:a√2 where the 2x=a√2
Re: Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a   [#permalink] 27 Feb 2019, 17:13
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