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In the figure above, V represents an observation point at on

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In the figure above, V represents an observation point at on [#permalink] New post 19 Dec 2012, 05:05
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Question Stats:

83% (02:27) correct 16% (01:54) wrong based on 121 sessions
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observation.png
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In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) 10-5\sqrt{3}
(B) 10-5\sqrt{2}
(C) 2
(D) 2 1/2
(E) 4
[Reveal] Spoiler: OA
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Re: In the figure above, V represents an observation point at on [#permalink] New post 19 Dec 2012, 05:09
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In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) 10-5\sqrt{3}
(B) 10-5\sqrt{2}
(C) 2
(D) 2 1/2
(E) 4

Attachment:
observation2.png
observation2.png [ 12.99 KiB | Viewed 1858 times ]

PR=\sqrt{VR^2-VP^2}=\sqrt{10^2-5^2}=5\sqrt{3};

Thus, RS=PS-PR=10-5\sqrt{3}.

Answer: A.
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Re: In the figure above, V represents an observation point at on [#permalink] New post 17 Nov 2013, 19:38
No need of using Pythagorean theorem. Observe triangle VPR. VP:VR=5:10=1:2. Angle opposite VR is 90. When does this happen? It happens only when VPR is a 30-60-90 triangle. So, VP:VR:PR=5:10:5\sqrt{3}.So, answer is 10-5\sqrt{3}
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Re: In the figure above, V represents an observation point at on [#permalink] New post 16 Apr 2014, 10:04
madn800 wrote:
No need of using Pythagorean theorem. Observe triangle VPR. VP:VR=5:10=1:2. Angle opposite VR is 90. When does this happen? It happens only when VPR is a 30-60-90 triangle. So, VP:VR:PR=5:10:5\sqrt{3}.So, answer is 10-5\sqrt{3}


How can you determine this is a 30-60-90 and not a 45-45-90?
Re: In the figure above, V represents an observation point at on   [#permalink] 16 Apr 2014, 10:04
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