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# In triangle ABC, if BC = 3 and AC = 4, then what is the

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Intern
Joined: 12 May 2014
Posts: 4
GMAT Date: 09-30-2014
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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30 Mar 2015, 07:52
enigma123 wrote:
Attachment:
Triangle.jpg
In triangle ABC, if BC = 3 and AC = 4, then what is the length of segment CD?

A. 3
B. 15/4
C. 5
D. 16/3
E. 20/3

use Pythagorean formula
BA=5

tri BAC is similiar to tri BDA

BD/BA====BA/BC

(X+3)/5===5/3
X=16/3
bingo
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Joined: 03 May 2013
Posts: 69
In triangle ABC, if BC = 3 and AC = 4, then what is the length of seg  [#permalink]

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27 May 2015, 21:07
[img]
Image[/img]
In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD?

A. 3
b. 15/4
C. 5
D. 16/3
E. 20/3

in-triangle-abc-to-the-right-if-bc-3-and-ac-4-then-88061.html

this has been discussed over the above given link, however i have a doubt and this topic was locked there , that's why opening new thread

Hi Bunuel,

I got it, three triangles are similar but Please explain how you deduce that angle BAC = angle ADC in two smaller triangles , I mean how you deduce that which one is height and which one is base of two smaller triangles

However by further drilling
all three triangles abc, acd & abd are similar.
so, 4/3=cd/4 ... cd = 16/3

it can't be 4/3=4/cd ... cd = 3, because in that case 5^2+5^2=6^2 is not true
I got to know which side is proportional to which side in smaller triangles , My query , isn’t this is a straight forward way to analyze which is base and which one is height of two smaller triangles
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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the length of seg  [#permalink]

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27 May 2015, 21:17
I guess Bunuel will take your question since it's directed to him so not responding to that.

Meanwhile, check out this question: in-the-diagram-above-pqr-is-a-right-angle-and-qs-is-131991.html#p1530394
Very similar figure. I have explained how you should find similarity - by naming the three triangles appropriately. Then it is obvious which angles are the equal angles and which sides are corresponding sides.
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Posts: 50042
In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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28 May 2015, 04:11
vipulgoel wrote:
[img]
Image[/img]
In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD?

A. 3
b. 15/4
C. 5
D. 16/3
E. 20/3

in-triangle-abc-to-the-right-if-bc-3-and-ac-4-then-88061.html

this has been discussed over the above given link, however i have a doubt and this topic was locked there , that's why opening new thread

Hi Bunuel,

I got it, three triangles are similar but Please explain how you deduce that angle BAC = angle ADC in two smaller triangles , I mean how you deduce that which one is height and which one is base of two smaller triangles

However by further drilling
all three triangles abc, acd & abd are similar.
so, 4/3=cd/4 ... cd = 16/3

it can't be 4/3=4/cd ... cd = 3, because in that case 5^2+5^2=6^2 is not true
I got to know which side is proportional to which side in smaller triangles , My query , isn’t this is a straight forward way to analyze which is base and which one is height of two smaller triangles

Merging topics.

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Manager
Joined: 03 May 2013
Posts: 69
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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28 May 2015, 11:55
Thanks Karishma and Bunuel, for wonderful explanation , I got it
Manager
Joined: 04 Jan 2014
Posts: 87
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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02 Jun 2015, 06:25
1
Hi Bunuel,

please explain me the correlation between 30-60-90(1:sq(3):2), 45-45-90(1:1:sq(2)) with pythagorean triplets(3-4-5, 7-24-25). I am confused because if we have a 90deg triangle, and 2 sides 3,4 we can put other side as 5? If so then it becomes 30-60-90 triangle right? then why we are not able to correlate 1:sq(3):2 with 3:4:5?
because we need to commonly multiply the ratio, so if 1*3 then sq(3) must also multiply by 3 which is not equal to 4..

Because I had tried an another approach which gives a wrong ans... Need clarification.. If ABC is a right triangle with 3,4 then other side must be 5. So Angle BAC will be 30 deg. which makes Ang CAD as 60 and CDA as 30.. So we have 30-60-90 triangle on ACD. If thats the case, then CD must be 4*sqrt(3) right? what's wrong in my approach?

Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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02 Jun 2015, 06:33
1
sheolokesh wrote:
Hi Bunuel,

please explain me the correlation between 30-60-90(1:sq(3):2), 45-45-90(1:1:sq(2)) with pythagorean triplets(3-4-5, 7-24-25). I am confused because if we have a 90deg triangle, and 2 sides 3,4 we can put other side as 5? If so then it becomes 30-60-90 triangle right? then why we are not able to correlate 1:sq(3):2 with 3:4:5?
because we need to commonly multiply the ratio, so if 1*3 then sq(3) must also multiply by 3 which is not equal to 4..

Because I had tried an another approach which gives a wrong ans... Need clarification.. If ABC is a right triangle with 3,4 then other side must be 5. So Angle BAC will be 30 deg. which makes Ang CAD as 60 and CDA as 30.. So we have 30-60-90 triangle on ACD. If thats the case, then CD must be 4*sqrt(3) right? what's wrong in my approach?

sheolokesh wrote:
if we have a 90deg triangle, and 2 sides 3,4 we can put other side as 5

Yes. If 3 and 4 are legs of a right triangle, then hypotenuse is 5.

sheolokesh wrote:
If so then it becomes 30-60-90 triangle right?

No. The angles in 3-4-5 right triangle are NOT 30°-60°-90°. They are ~53° - ~37 ° - 90°.
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Posts: 87
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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02 Jun 2015, 07:00
So all triplets has 37-53-90 degrees right? Its better not to confuse triplets with 30-60-90 or 45-45-90 then..
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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02 Jun 2015, 07:07
sheolokesh wrote:
So all triplets has 37-53-90 degrees right? Its better not to confuse triplets with 30-60-90 or 45-45-90 then..

No. In 3-4-5, 6-8-10, 9-12-15, ... right triangles angles will be ~53° - ~37 ° - 90°. But for example, in 5-12-13 right triangle angles are 23°-67°-90°.
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Posts: 40
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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07 Jul 2016, 00:43
It a very important concept i believe:
Perpendicular to the hypotenuse in a right angled triangle is the geometric mean of the two divisions of the hypotenuse.

Ac^2=BC*CD
4^2=3*CD
so CD=16/3
Intern
Joined: 17 Sep 2016
Posts: 3
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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11 Oct 2016, 09:37
Hey Could any one please tell me if my approach is correct! I used trigonometry!

Approach below:
Consider triangle ABC
cosθ = 3/5 (base/hyp)........(1)
Consider triangle ABD
cosθ = 5/(3+CD).........(2)

Equate (1) and (2)

3/5=5/(3+CD)
3CD+9= 25 ====> CD=16/3
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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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11 Oct 2016, 10:06
shivamtt770 wrote:
Hey Could any one please tell me if my approach is correct! I used trigonometry!

Approach below:
Consider triangle ABC
cosθ = 3/5 (base/hyp)........(1)
Consider triangle ABD
cosθ = 5/(3+CD).........(2)

Equate (1) and (2)

3/5=5/(3+CD)
3CD+9= 25 ====> CD=16/3

yes, this is another approach to solve this question. Every approach is correct if you are getting a right answer in shortest span of time.
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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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11 Oct 2016, 11:24
Quote:
In triangle ABC, if BC = 3 and AC = 4, then what is the length of segment CD?

A. 3
B. 15/4
C. 5
D. 16/3
E. 20/3

As depicted in the figure, AB^2 = 3^2 + 4^2 = 5^2
i.e. AB = 5

NOW TRIANGLE ABC AND TRIANGLE ACD ARE SIMILAR TRIANGLE

So the ratio of their corresponding sides will be equal

AC/BC = CD/AC

4/3 = CD/4

i.e. CD = 16/3

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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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30 Sep 2018, 02:24
How the angle BAC is equal to angle ADC
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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the  [#permalink]

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30 Sep 2018, 05:38
sudhanshutiwari wrote:
How the angle BAC is equal to angle ADC

sudhanshutiwari
Take bigger triangle ABD and mark Angles as 90-x - (90-x)

Now look at triangle ACD, one of the angle you can already see marked is (90-x) one angle is 90 so third angle becomes x (if you subtract other two angles from 180)

Similarly, look at triangle ABC, one of the angle you can already see marked is x one angle is 90 so third angle becomes 90-x (if you subtract other two angles from 180)

This is how, we figure out that angle BAC is equal to angle ADC

I hope this helps
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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the &nbs [#permalink] 30 Sep 2018, 05:38

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