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

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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?

Re: In the figure above, V represents an observation point at on [#permalink]
19 Dec 2012, 05:09

Expert's post

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?

Re: In the figure above, V represents an observation point at on [#permalink]
17 Nov 2013, 19:38

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This post received KUDOS

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\(\sqrt{3}\)

Re: In the figure above, V represents an observation point at on [#permalink]
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]
18 Apr 2014, 10:05

Expert's post

atl12688 wrote:

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?

In right triangle VPR the ratio of one side (VP) to hypotenuse (VR) is 1:2. This only happens for 30-60-90 right triangle.

MUST KNOW FOR THE GMAT: • A right triangle where the angles are 30°, 60°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio \(1 : \sqrt{3}: 2\). Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

• A right triangle where the angles are 45°, 45°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should also commit to memory is: The sides are always in the ratio \(1 : 1 : \sqrt{2}\). With the \(\sqrt{2}\) being the hypotenuse (longest side). This can be derived from Pythagoras' Theorem. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles.

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