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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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Lines m and n are parallel. If the length of AB is 12, what is the per  [#permalink]

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New post 13 Jul 2020, 01:14
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Re: Lines m and n are parallel. If the length of AB is 12, what is the per  [#permalink]

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New post 13 Jul 2020, 01:33
1
Supplementary angle to 150 = 180-150 = 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  [#permalink]

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New post 13 Jul 2020, 01:36
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IMO B
Let AD be the perpendicular distance
So, angle BAD = 90 - (180-150) = 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  [#permalink]

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New post 13 Jul 2020, 02:07
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lets draw a perpendicular to line m from point B
angle BAC =30 ,angle BCA=90 , thus angle ABC=60
sides of 30-60-90 triangle are in ratio of 1:√3:2

AB=12 MEANS , BC=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  [#permalink]

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New post 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  [#permalink]

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New post 13 Jul 2020, 11:04
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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  [#permalink]

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New post 13 Jul 2020, 15:28
If we draw a perpendicular from point B to line m, we will get a 30-60-90 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  [#permalink]

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New post 13 Jul 2020, 19:10
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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  [#permalink]

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New post 13 Jul 2020, 20:32
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Ans: B
Draw a perpendicular between m and n.So BX is the perpendicular.
angle BAX=180-150=30, angle BXA=90 & angle ABX=60
so it's a 90-60-30 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  [#permalink]

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New post 13 Jul 2020, 20:46
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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=180-150=30 degrees. Therefore ABC is a 90-60-30 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  [#permalink]

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New post 14 Jul 2020, 06:31
Draw a perpendicular from B to C. This gives us a triangle ABC.
Let's calculate for ∠A = 180-150 = 30
∠C = 90. This gives us a 30-60-90 triangle. Hence, using ratio 1x:√3x:2x.
Given, AB -> 2x = 12 -> x=6 -> BC
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Lines m and n are parallel. If the length of AB is 12, what is the per   [#permalink] 14 Jul 2020, 06:31

Lines m and n are parallel. If the length of AB is 12, what is the per

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