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In the figure above, \(V\) represents an observation point

Expert replies
by AAPL » Sun Oct 20, 2019 12:18 am
Official Guide

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

OA A
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Source: — Problem Solving |

by Jay@ManhattanReview » Mon Oct 21, 2019 4:34 am
AAPL wrote:Official Guide

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

OA A
Say the perpendicular dropped from point V to the extended line RS is O; thus, OV and RS are perpendicular to each other.

Thus, ∆OVR is a right-angled triangle. And, OR^2 = VR^2 – OV^2 = 10^2 – 5^2 = √75

=> OR = 5√3

Thus, RS = OS – OR = 10 – 5√3

The correct answer: A

Hope this helps!

-Jay
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