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Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 01:14
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Competition Mode Question Lines m and n are parallel. If the length of AB is 12, what is the perpendicular distance between m and n ? A. \(4\sqrt{3}\) B. 6 C. \(6\sqrt{2}\) D. \(6\sqrt{3}\) E. 12 Attachment:
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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 01:33
Supplementary angle to 150 = 180150 = 30 DRAWING A PERPENDICULAR FROM LINE N TO M, MEETING M AT C Such that ABC is a right angle triangle. Where angle A = 30°, B = 90°, C = 60°
Therefore ABC is a 30,60,90 right angle triangle.where sides are x,√3x and 2x(hypotenuse)
We want to find perpendicular height or X. 2x = 12 X = 6
Answer is B
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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 01:36
IMO B Let AD be the perpendicular distance So, angle BAD = 90  (180150) = 60
In traingle ADB, AB=12 Cos angle BAD= AD/AB So, AD= AB cos 60 = 12 x 1/2 = 6 Ans B
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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 02:07
lets draw a perpendicular to line m from point B angle BAC =30 ,angle BCA=90 , thus angle ABC=60 sides of 306090 triangle are in ratio of 1:√3:2 AB=12 MEANS , BC=6ANS:B
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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 07:08
Let the perpendicular distance between m and n line be h , i.e , AC. BAC = 90  30 = 60 In Triangle ABC, \(cos BAC = \frac{AC}{AB}\)
\(=> cos 60 = \frac{h}{12}\)
\(=> \frac{1}{2} = \frac{h}{12}\)
\(=> h = 6\)
Hence, OA is (B).



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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 11:04
OA B ?
Let Perpendicular = BC , C on line m.
In triangle ABC, angle A = 30. AB = 12.
Now, sin30 = 1/2 = perpendicular /Hypotenuse = perpendicular distance/12
> 1/2 = distance /12
> Distance b/w m and n = 6.



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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 15:28
If we draw a perpendicular from point B to line m, we will get a 306090 degree right triangle, the hypotenuse is AB = 12, the perpendicular is opposite to the 30 degree angle, so applying Pythagorean theory, we can find the length of the perpendicular as 6.
B is the answer.



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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 19:10
Let us draw a line from point A to the line n meeting the line n at 90 degrees (perpendicular) and let us call this point C.
Now we have a Triangle ABC where angle ACB = 90 (perpendicular)  (A)
Also. line m is parallel to line n.
Therefore, angle ABn = 150 (congruent angles)
This gives us Angle ABC = 180  150 (Straight Line) = 30  (B)
Hence, angle BAC = 180  ( 90 + 30 ) = 60  (C)
We also have AB = 12.
Now, AC (perpendicular) = ABcos60 (60 is the angle between AB and AC) = 12*(1/2) = 6
Hence, AC = 6. The answer is Option (B)



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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 20:32
Ans: B Draw a perpendicular between m and n.So BX is the perpendicular. angle BAX=180150=30, angle BXA=90 & angle ABX=60 so it's a 906030 triangle where sides are in 2:root3 :1 ratio now, 2x=12,x=6 so BX=6



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Re: Lines m and n are parallel. If the length of AB is 12, what is the per
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13 Jul 2020, 20:46
Draw a perpendicular from B to line line m and let that perpendicular be BC.So we have a rt angle triangle ABC where AB(hypotenuse)= 12, angle BAC=180150=30 degrees. Therefore ABC is a 906030 triangle and the sides are in the ratio of 2:root 3:1 hence, BC=AB/2 BC=6 option B



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Lines m and n are parallel. If the length of AB is 12, what is the per
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14 Jul 2020, 06:31
Draw a perpendicular from B to C. This gives us a triangle ABC. Let's calculate for ∠A = 180150 = 30 ∠C = 90. This gives us a 306090 triangle. Hence, using ratio 1x:√3x:2x. Given, AB > 2x = 12 > x=6 > BC




Lines m and n are parallel. If the length of AB is 12, what is the per
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14 Jul 2020, 06:31




