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Observation point - Geometry

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by GmatGreen » Fri Feb 21, 2014 8:26 am
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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 - 5root(3)
B) 10 - 5root(2)
C) 2
D) 2.5
4) 4
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by Patrick_GMATFix » Fri Feb 21, 2014 8:41 am
As with most geometry questions, this one can be solved more easily if you take the time to draw and label a figure on your scrap paper. The full solution below is taken from the GMATFix App.

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by [email protected] » Fri Feb 21, 2014 11:35 am
Hi GmatGreen,

Geometry questions are usually based around common shapes that you know (and their respective formulas). I'm going to offer you a hint as to how to solve this problem so that you can try it on your own.

If you draw a line from V to R, you'll end up with a right triangle.
If you draw a line from V to S, you'll end up with a bigger right triangle.

Using the Pythagorean Theorem, you should be able to figure out the missing sides in those right triangles....and then use those numbers to figure out the length of RS....

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by mcdesty » Thu Jul 10, 2014 8:53 am
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by Scott@TargetTestPrep » Wed Jul 08, 2015 4:48 am
GmatGreen wrote:Image
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 - 5root(3)
B) 10 - 5root(2)
C) 2
D) 2.5
4) 4
Solution:

We are being asked to determine the length of RS. To determine this length we need to know the length from point R to the right angle in the given figure. If we label the point at the right angle as T, we see that we need to determine the length of TR.

If we draw a line segment connecting V and R, we will see that VR, VT and TR create a right triangle. Furthermore, we are told in the question stem that VR (the hypotenuse) is 10, and that one of the sides, VT, is 5, so we now plug these values into the Pythagorean Theorem.

TR^2 + VT^2 = VR^2

TR ^2 + 5^2 = 10^2

TR ^2 + 25 = 100

TR ^2 = 75

TR = √75

TR = √25 x √3

TR = 5√3

So TR is 5√3. We subtract this from the total length TS, which is 10, to determine the length from R to S:

10 - 5√3

Answer: A

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