Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62379

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
02 Jun 2015, 05:33
sheolokesh wrote: Hi Bunuel,
please explain me the correlation between 306090(1:sq(3):2), 454590(1:1:sq(2)) with pythagorean triplets(345, 72425). 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 306090 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 306090 triangle on ACD. If thats the case, then CD must be 4*sqrt(3) right? what's wrong in my approach?
Please help.. 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 306090 triangle right? No. The angles in 345 right triangle are NOT 30°60°90°. They are ~53°  ~37 °  90°.
_________________



Manager
Joined: 04 Jan 2014
Posts: 68

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
02 Jun 2015, 06:00
So all triplets has 375390 degrees right? Its better not to confuse triplets with 306090 or 454590 then..



Math Expert
Joined: 02 Sep 2009
Posts: 62379

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
02 Jun 2015, 06:07
sheolokesh wrote: So all triplets has 375390 degrees right? Its better not to confuse triplets with 306090 or 454590 then.. No. In 345, 6810, 91215, ... right triangles angles will be ~53°  ~37 °  90°. But for example, in 51213 right triangle angles are 23°67°90°.
_________________



Intern
Joined: 17 Sep 2016
Posts: 3

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



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3414
Location: India
GMAT: QUANT EXPERT
WE: Education (Education)

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
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 Answer: option D
Attachments
File comment: www.GMATinsight.com
Sol1.jpg [ 25.87 KiB  Viewed 11860 times ]
_________________
Prosper!!!GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) email: info@GMATinsight.com l Call : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West DelhiClick Here for Uneditable GOOGLE reviewsClick here for Our VERBAL & QUANT private tutoring package detailsMy Recent Posts Q1IntegerDivisibility l Q2Inequality DS l Q3Standard Deviation l Q4Functions ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION



Intern
Joined: 22 Sep 2018
Posts: 1

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
30 Sep 2018, 01:24
How the angle BAC is equal to angle ADC



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3414
Location: India
GMAT: QUANT EXPERT
WE: Education (Education)

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
30 Sep 2018, 04:38
sudhanshutiwari wrote: How the angle BAC is equal to angle ADC sudhanshutiwariTake bigger triangle ABD and mark Angles as 90x  (90x) Now look at triangle ACD, one of the angle you can already see marked is (90x) 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 90x (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
_________________
Prosper!!!GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) email: info@GMATinsight.com l Call : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West DelhiClick Here for Uneditable GOOGLE reviewsClick here for Our VERBAL & QUANT private tutoring package detailsMy Recent Posts Q1IntegerDivisibility l Q2Inequality DS l Q3Standard Deviation l Q4Functions ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10229
Location: Pune, India

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
24 Jun 2019, 03:59
VeritasKarishma wrote: Both smaller triangles are similar to the large triangle. So they are similar to each other too.
In triangles BAD and BCA, Angle BAD = BCA (90 degrees) and angle B is common in both So by AA, triangles BAD and BCA are similar
Similarly, in triangles BAD and ADC, angle BAD = ACD (90 degrees) and angle D is common in both So by AA, triangles BAD and ACD are similar
So triangle BAD is similar to triangle BCA and ACD so triangle BCA is similar to triangle ACD too. Responding to a pm: Quote: Can you explain why it's not BCA is similar to DCA? Since according to the image, A is the same for both triangles and C is the same, so shouldn't it be BCA and DCA? Note that angles BCA and DCA are both 90 degrees so that's fine but angles BAC and DAC are not equal. These are two distinct angles and can take any values. Using the logic I have discussed in my solution, we find that triangle BCA is similar to triangle ACD.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 21 Feb 2017
Posts: 208

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
23 Mar 2020, 03:08
VeritasKarishma wrote: VeritasKarishma wrote: Both smaller triangles are similar to the large triangle. So they are similar to each other too.
In triangles BAD and BCA, Angle BAD = BCA (90 degrees) and angle B is common in both So by AA, triangles BAD and BCA are similar
Similarly, in triangles BAD and ADC, angle BAD = ACD (90 degrees) and angle D is common in both So by AA, triangles BAD and ACD are similar
So triangle BAD is similar to triangle BCA and ACD so triangle BCA is similar to triangle ACD too. Responding to a pm: Quote: Can you explain why it's not BCA is similar to DCA? Since according to the image, A is the same for both triangles and C is the same, so shouldn't it be BCA and DCA? Note that angles BCA and DCA are both 90 degrees so that's fine but angles BAC and DAC are not equal. These are two distinct angles and can take any values. Using the logic I have discussed in my solution, we find that triangle BCA is similar to triangle ACD. Hi VeritasKarishma. I understood that BAC and DAC are not equal cus we don't know whether the bisector AC is bisecting angle A equally; but how do we establish angle B to be similar to angle A?? did we derive it from the above ratios?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10229
Location: Pune, India

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
23 Mar 2020, 22:05
Kritisood wrote: VeritasKarishma wrote: VeritasKarishma wrote: Both smaller triangles are similar to the large triangle. So they are similar to each other too.
In triangles BAD and BCA, Angle BAD = BCA (90 degrees) and angle B is common in both So by AA, triangles BAD and BCA are similar
Similarly, in triangles BAD and ADC, angle BAD = ACD (90 degrees) and angle D is common in both So by AA, triangles BAD and ACD are similar
So triangle BAD is similar to triangle BCA and ACD so triangle BCA is similar to triangle ACD too. Responding to a pm: Quote: Can you explain why it's not BCA is similar to DCA? Since according to the image, A is the same for both triangles and C is the same, so shouldn't it be BCA and DCA? Note that angles BCA and DCA are both 90 degrees so that's fine but angles BAC and DAC are not equal. These are two distinct angles and can take any values. Using the logic I have discussed in my solution, we find that triangle BCA is similar to triangle ACD. Hi VeritasKarishma. I understood that BAC and DAC are not equal cus we don't know whether the bisector AC is bisecting angle A equally; but how do we establish angle B to be similar to angle A?? did we derive it from the above ratios? This is a standard figure that begs you to think about similar triangle. Some such figures are given in this post on Veritas blog: https://www.veritasprep.com/blog/2014/0 ... thegmat/Here, triangle CBA is similar to CDA and both are similar to triangle ABD. If you want to see how, note this: Between triangles CBA and ABD, Angle C is 90 and angle BAD are 90 each. Angle B is common to both. So by AA, both triangles are similar. Between triangles CDA and ADB, Angles ACD and BAD are 90 each. Angle D is common to both. So by AA, both triangles are similar. Between triangles CBA and CAD, Angle C is 90. Now say angle BAC is x, then angle CAD is (90x). Then in triangle CAD, angle D must be x. Hence angle BAC = angle D So by AA, both triangles are similar.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 21 Feb 2017
Posts: 208

Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
Show Tags
24 Mar 2020, 03:10
VeritasKarishma wrote: Kritisood wrote: Responding to a pm: Quote: Can you explain why it's not BCA is similar to DCA? Since according to the image, A is the same for both triangles and C is the same, so shouldn't it be BCA and DCA? Note that angles BCA and DCA are both 90 degrees so that's fine but angles BAC and DAC are not equal. These are two distinct angles and can take any values. Using the logic I have discussed in my solution, we find that triangle BCA is similar to triangle ACD. Hi VeritasKarishma. I understood that BAC and DAC are not equal cus we don't know whether the bisector AC is bisecting angle A equally; but how do we establish angle B to be similar to angle A?? did we derive it from the above ratios? This is a standard figure that begs you to think about similar triangle. Some such figures are given in this post on Veritas blog: https://www.veritasprep.com/blog/2014/0 ... thegmat/Here, triangle CBA is similar to CDA and both are similar to triangle ABD. If you want to see how, note this: Between triangles CBA and ABD, Angle C is 90 and angle BAD are 90 each. Angle B is common to both. So by AA, both triangles are similar. Between triangles CDA and ADB, Angles ACD and BAD are 90 each. Angle D is common to both. So by AA, both triangles are similar. Between triangles CBA and CAD, Angle C is 90. Now say angle BAC is x, then angle CAD is (90x). Then in triangle CAD, angle D must be x. Hence angle BAC = angle D So by AA, both triangles are similar.[/quote] Oh... understood now.




Re: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the
[#permalink]
24 Mar 2020, 03:10



Go to page
Previous
1 2
[ 31 posts ]



