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

Question

https://gmatclub.com/forum/download/file.php?id=61768 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 1.png

Dashingnightmare · Answer

since entire figure will be a square , hence angle ACD=90
ACF =45(half of 90)
ACG = 45/2 approx 22.5 ,
 hence B.

nick1816 · Answer

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

Thelegend2631 · Answer

Condition is true for only isosceles and equilateral triangle.

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Thelegend2631 · Answer

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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ShaikhMoice · Answer

Is there a way to solve the question without Trignometry.

Thnaks in Advance

Thelegend2631 · Answer

With or without trigonometry?

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ShubhadeepB · Answer

Bunuel 
Can you please post a detailed explanation for this?

ShaikhMoice · Answer

Without. Type thanks edited my post

ShaikhMoice · Answer

Without, edited my post thanks

PrinceJ · Answer

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

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

Prep Toolkit

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