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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of

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Bunuel
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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   19 May 2021, 06:45
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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of the following best approximates ∠ACG ?

A. 14º
B. 24º
C. 34º
D. 44º
E. 54º

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Dashingnightmare
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   19 May 2021, 11:40
since entire figure will be a square , hence angle ACD=90
ACF =45(half of 90)
ACG = 45/2 approx 22.5 ,
hence B.
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   19 May 2021, 19:56
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tan(ACG) = 1/4

\(tan30= \frac{1}{\sqrt{3}}\)

We can eliminate C, D and E

tan15 = \(\frac{1-cos30}{sin30 }\)~ \(\frac{0.13}{0.5 }\)~ 0.25

A


Bunuel wrote:

ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of the following best approximates ∠ACG ?

A. 14º
B. 24º
C. 34º
D. 44º
E. 54º

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Attachment:
1.png
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   19 May 2021, 22:01
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Dashingnightmare wrote:
since entire figure will be a square , hence angle ACD=90
ACF =45(half of 90)
ACG = 45/2 approx 22.5 ,
hence B.


Condition is true for only isosceles and equilateral triangle.

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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   19 May 2021, 22:07
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Bunuel wrote:

ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of the following best approximates ∠ACG ?

A. 14º
B. 24º
C. 34º
D. 44º
E. 54º

Show Spoiler
Attachment:
1.png



Since tan C = 1/4.
1/4 < 1/1.732. ( Tan 30)

We can assume Angle to be closer to half of 30 SINCE Actual values of Tan indicates similar difference.

However, lets find out Tan 15

Tan ( 45-30) = (tan 45-tan30)/(1+ tan30*tan45)

Tan 15 = (√3-1)/(√3+1) = 0.732²/2
Tan 15 = 0.51~/2 = 0.25~
Hence A!

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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   Updated on: 10 Sep 2021, 23:56
Is there a way to solve the question without Trignometry.

Thnaks in Advance

Originally posted by ShaikhMoice on 10 Sep 2021, 23:47.
Last edited by ShaikhMoice on 10 Sep 2021, 23:56, edited 1 time in total.
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   10 Sep 2021, 23:50
ShaikhMoice wrote:
Is there a way to solve the question with Trignometry.

Thnaks in Advance



With or without trigonometry?

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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   10 Sep 2021, 23:55
Bunuel
Can you please post a detailed explanation for this?
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   10 Sep 2021, 23:57
hD13 wrote:
ShaikhMoice wrote:
Is there a way to solve the question with Trignometry.

Thnaks in Advance



With or without trigonometry?

Posted from my mobile device


Without. Type thanks edited my post
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Re: ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   10 Sep 2021, 23:57
hD13 wrote:
ShaikhMoice wrote:
Is there a way to solve the question with Trignometry.

Thnaks in Advance



With or without trigonometry?

Posted from my mobile device


Without, edited my post thanks
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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink] New post   11 Sep 2021, 00:21
ShaikhMoice wrote:
Is there a way to solve the question without Trignometry.

Thnaks in Advance


Consider the square BCDE and a point G' which is midpoint of side BE.
Angle BCE will be 45° and by logic angle BCG' would have been 22.5°(half of 45).
Now, beacausee of point G the angle BCG' is further reduced. So angle BCG will be less than 22.5°.
Only option A is valid.

The question could be solved since only one option was less than 22.5, otherwise you may need trigo as per other explanations.

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ABEF and BCDE are congruent squares. G is a midpoint of AF. Which of [#permalink]
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