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Manager  Joined: 11 Jan 2006
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Location: Arkansas, US
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In the figure above, line AC represents a seesaw that is  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 51% (01:33) correct 49% (01:28) wrong based on 405 sessions

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In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?

(1) x = 30
(2) Point B is 5 feet above the ground.

Attachments fig1.doc [20.5 KiB]

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Originally posted by Raghavender on 03 Oct 2006, 05:34.
Last edited by Bunuel on 29 Nov 2013, 02:25, edited 1 time in total.
Edited the question and added the OA.
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Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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Hi All,

For those of you who are not comfortable with the concept of similar triangles and its application, this question can be solved using application of simple trigonometric ratios. In triangle ABD which is right angled at D, we can use $$Sin x = \frac{BD}{AB.}$$

Similarly, in triangle ACE which is right angled at E, we can use $$Sin x = \frac{CE}{AC}$$

From the above two equations, we can write $$\frac{BD}{AB} = \frac{CE}{AC}$$ i.e. $$CE = \frac{(BD * AC)}{AB.}$$

Since $$AC = 2AB$$, we can write $$CE = 2BD$$.

So, for finding the height of point C from the ground we just need to know the height of point B from the ground.

We see that st-II provides us the height of B. Thus statement-II alone is sufficient to answer the question.

You can try out a similar question at a-squirrel-climbs-a-straight-wire-from-point-a-to-point-c-if-b-is-the-195315.html#p1517662

Hope its clear!

Regards
Harsh
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Statement 2 alone is suff.
lets say: BA= x
then CA = 2x (since B is the mid point of CA)
Triangle ACD(D is the point where the perpendicular dropped from C touches the ground) is similar to triangle ABE(E is the point where the perpendicular dropped from C touches the ground).
Therefore x/5=2x/z
or z=10
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20. In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?
(1) x = 30
(2) Point B is 5 feet above the ground.

A & B are unsufficient.

Combining

Sin 30(degree) = 5/AB
so AB can be determine and hence AC, since AC=2AB.

If we draw a perpendicula from line A which touches point C and call that point (on line A) D.

So, Sin 30 = AD/2AB
Director  Joined: 23 Jun 2005
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This one had me stumped. But, B it is, as others have explained before.
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It is B.
Apply property of similar triangles.........
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Originally posted by cicerone on 05 Oct 2006, 01:03.
Last edited by cicerone on 25 Sep 2008, 01:30, edited 1 time in total.
Manager  Joined: 11 Jan 2006
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Gud explanation 800_gal...

Thanks for that..hahaa..completely forgot about the similar triangles properties...gotto revise it now...
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Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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Raghavender wrote:
20. In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?
(1) x = 30
(2) Point B is 5 feet above the ground.

Is there anyway someone can put the picture on the problem so we don't have to open it every time?

Much appreciated!
Cheers
J Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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jlgdr wrote:
Raghavender wrote:
20. In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?
(1) x = 30
(2) Point B is 5 feet above the ground.

Is there anyway someone can put the picture on the problem so we don't have to open it every time?

Much appreciated!
Cheers
J ______________
Done.
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In the figure above, line AC represents a seesaw that is  [#permalink]

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What i don't get is why we can assume that the two triangles are similar just because AB = BC?

I mean it looks similar, but why can we apply that?
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In the figure above, line AC represents a seesaw that is  [#permalink]

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noTh1ng wrote:
What i don't get is why we can assume that the two triangles are similar just because AB = BC?

I mean i looks similar, but why can we apply that?

Refer to the attached figure for description of the points.

BD and CE are perpendicular to AE.

So, in triangles ABD and ACE, angle A is common angle to both the triangles, $$\angle{ADB} = \angle{AEC} = 90$$ and $$\angle {ABD} = \angle{ACE}$$ (BD || CE)

Thus triangles ABD ad ACE are similar by AA (or angle -angle similarity theorem)

Thus, by similarity

AB/ AC = BD / CE

Given BD = 5 and AB = 0.5*AC

Thus CE = 10. Hence, Statement 2 is sufficient.

Per statement 1, x =30 does not provide us any other useful information.

Thus B is the correct answer.

Hope this helps.
Attachments Similar triangles.jpg [ 11.3 KiB | Viewed 5012 times ]

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Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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noTh1ng wrote:
What i don't get is why we can assume that the two triangles are similar just because AB = BC?

I mean it looks similar, but why can we apply that?

Attachment: Untitled.png [ 21.95 KiB | Viewed 5006 times ]

You can use three rules to prove that the triangles are similar.
1. AA- two angles are equal.
2. SSS- All three sides are proportional to each other.
3. SAS- One angle is equal and the two adjacent sides are proportional.

In this case, you know two angles are equal, x and the 90. Since the height of a point is being measured.

Hope it helps.
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Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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thx akhilbajaj ; good for memorizing this stuff Retired Moderator V
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Re: In the figure above, line AC represents a seesaw that is  [#permalink]

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Project DS Butler: Day 61: Data Sufficiency (DS121)

Bumping for DS butler Projec
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In the figure above, line AC represents a seesaw that is  [#permalink]

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Raghavender wrote:
Attachment:
Untitled.png
In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?

(1) x = 30
(2) Point B is 5 feet above the ground.

Use the midpoint theorem we studied in school/college.

In the triangle provided consider the points from B&C hitting the ground as D&E.

Hence we have two triangles -> ACE & ABD. Since B is the midpoint of AC and CE||BD from the midpoint theorem we know that D is the midpoint of AE and also CE=2BD.

Actually, the midpoint theorem stems from the concept of similar triangles and all the sides in the 2 triangles will be in the ratio 1:2

hence CE = 2BD, AC = 2AB = 2BC, AE = 2DE = 2AD

So we can conclude if we know any one of the sides we can know the corresponding side of the other triangle. Here we know BD and hence can calculate CE.

Hence B is the correct answer.
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In the figure above, line AC represents a seesaw that is  [#permalink]

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Raghavender wrote:
Attachment:
Untitled.png
In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?

(1) x = 30
(2) Point B is 5 feet above the ground.

Or simply use Pythagoras theorem to the smaller triangle and larger triangle .
then equate the sides with known values to find that large triangle Ht is twice the smaller triangle.
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T-Twitted In the figure above, line AC represents a seesaw that is   [#permalink] 20 Sep 2019, 09:40
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