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In the triangle ABC shown above, what is the value of ∠ACB

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saswata4s
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In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   Updated on: 23 Apr 2018, 02:40
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In the triangle ABC shown above, what is the value of ∠ACB?

(1) AB^2 + BC^2 = AC^2
(2) The length of sides AB and BC is 6 and 6 units respectively


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C

Originally posted by saswata4s on 23 Apr 2018, 02:31.
Last edited by Bunuel on 23 Apr 2018, 02:40, edited 2 times in total.
Edited the question.
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chetan2u
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 04:34
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saswata4s wrote:


In the triangle ABC shown above, what is the value of ∠ACB?

(1) AB^2 + BC^2 = AC^2
(2) The length of sides AB and BC is 6 and 6 units respectively


Show Spoiler
Attachment:
Figure 1.JPG



Don't get carried away by the sketch, angle B could be 90 or 91 or 95..

Let's see what each statement tells us..
I.. it tells us that it is a RIGHT angled triangle, so B=90
II.. it tells us that the triangle is isosceles triangle, so angle C=angle A..

Combined, we know it is 45-45-90 ∆
Sufficient

C
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 03:36
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saswata4s wrote:


In the triangle ABC shown above, what is the value of ∠ACB?

(1) AB^2 + BC^2 = AC^2
(2) The length of sides AB and BC is 6 and 6 units respectively


Show Spoiler
Attachment:
Figure 1.JPG


Statement 1: \(AB^2 + BC^2 = AC^2\) -- Pythagorean theorem is used to find the length of a side of a triangle if we're given the lengths of the other two sides. Therefore statement 1 is not sufficient to find the value of C (an angle) in triangle ACB.

Statement 2: The length of sides AB and BC is 6 and 6 units respectively -- since AB=BC triangle ACB has to be an isosceles triangle with B= 90 degrees, A= 45 degrees, and C = 45 degrees. Therefore statement 2 is sufficient.

IMHO, answer is B -- statement 2 alone is sufficient.
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 03:51
For Option B-- How do we conclude that B is 90 degree.
Answer should b C. Since Pythagorean theorem is applied which makes the angle B 90 degree.
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 03:59
prasang wrote:
For Option B-- How do we conclude that B is 90 degree.
Answer should b C. Since Pythagorean theorem is applied which makes the angle B 90 degree.



The angle opposite of side AB is C, and the angle opposite of side BC is A. We're given that AB = BC = 6. Therefore angles C and A must be 45 degrees each. We're left with angle B, which must be 90 degrees.
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 04:10
Wildflower wrote:
prasang wrote:
For Option B-- How do we conclude that B is 90 degree.
Answer should b C. Since Pythagorean theorem is applied which makes the angle B 90 degree.



The angle opposite of side AB is C, and the angle opposite of side BC is A. We're given that AB = BC = 6. Therefore angles C and A must be 45 degrees each. We're left with angle B, which must be 90 degrees.


Hi,
But how you came to the conclusion that angles C & A must be 45 degrees? I agree that Statement B gives us isoscles triangle but how it gives the angle measure?
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 05:06
prasang wrote:
For Option B-- How do we conclude that B is 90 degree.
Answer should b C. Since Pythagorean theorem is applied which makes the angle B 90 degree.


Got it, thank you! :thumbup:
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   23 Apr 2018, 05:07
rohitf23 wrote:
Wildflower wrote:
prasang wrote:
For Option B-- How do we conclude that B is 90 degree.
Answer should b C. Since Pythagorean theorem is applied which makes the angle B 90 degree.



The angle opposite of side AB is C, and the angle opposite of side BC is A. We're given that AB = BC = 6. Therefore angles C and A must be 45 degrees each. We're left with angle B, which must be 90 degrees.


Hi,
But how you came to the conclusion that angles C & A must be 45 degrees? I agree that Statement B gives us isoscles triangle but how it gives the angle measure?


Hi, you're right. I shouldn't have assumed. Thank you!
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   09 May 2018, 10:06
I) right triangle but don't know Bout other two sides
They can be equal then angle 45
If not different Angles
Insufficient

II)two sides equal
If all three equal then angle 60 as case of equilateral
Or they can be isosceles right triangle or isosceles non right triangle
Insufficient

Combining
Isosceles right triangle exists so angle 45 degree

Posted from my mobile device
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink] New post   19 Sep 2019, 08:38
Wildflower wrote:
saswata4s wrote:


In the triangle ABC shown above, what is the value of ∠ACB?

(1) AB^2 + BC^2 = AC^2
(2) The length of sides AB and BC is 6 and 6 units respectively


Show Spoiler
Attachment:
Figure 1.JPG


Statement 1: \(AB^2 + BC^2 = AC^2\) -- Pythagorean theorem is used to find the length of a side of a triangle if we're given the lengths of the other two sides. Therefore statement 1 is not sufficient to find the value of C (an angle) in triangle ACB.

Statement 2: The length of sides AB and BC is 6 and 6 units respectively -- since AB=BC triangle ACB has to be an isosceles triangle with B= 90 degrees, A= 45 degrees, and C = 45 degrees. Therefore statement 2 is sufficient.

IMHO, answer is B -- statement 2 alone is sufficient.


You dont know that angle b is 90. only from option a it can be decipehred that angle b is right angle
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Re: In the triangle ABC shown above, what is the value of ∠ACB [#permalink]
19 Sep 2019, 08:38
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