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In triangle ABC, if BC = 3 and AC = 4, then what is the length of segm

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Joined: 02 Sep 2009
Posts: 52431
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the length of segm  [#permalink]

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02 Jun 2015, 05:33
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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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the length of segm  [#permalink]

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02 Jun 2015, 06:00
So all triplets has 37-53-90 degrees right? Its better not to confuse triplets with 30-60-90 or 45-45-90 then..
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Joined: 02 Sep 2009
Posts: 52431
Re: In triangle ABC, if BC = 3 and AC = 4, then what is the length of segm  [#permalink]

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02 Jun 2015, 06:07
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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Re: In triangle ABC, if BC = 3 and AC = 4, then what is the length of segm  [#permalink]

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11 Oct 2016, 08:37
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 length of segm  [#permalink]

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11 Oct 2016, 10:24
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 length of segm  [#permalink]

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30 Sep 2018, 01:24
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 length of segm  [#permalink]

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30 Sep 2018, 04:38
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 length of segm &nbs [#permalink] 30 Sep 2018, 04:38

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