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The image of a star is projected onto a planetarium wall by

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The image of a star is projected onto a planetarium wall by [#permalink] New post   13 Sep 2020, 08:26
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The image of a star is projected onto a planetarium wall by a projector that sits atop a vertical 4-foot stand. If the projector is directed 30 degrees above the horizontal, and the image appears 16 feet above the level floor of the planetarium, then, in feet, how far is the projector from the wall?

A. \(12 \sqrt{2}\)

B. \(12 \sqrt{3}\)

C. \(16 \sqrt{2}\)

D. \(16 \sqrt{3}\)

E. \(24\)
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B
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Re: The image of a star is projected onto a planetarium wall by [#permalink] New post   29 Sep 2020, 10:32
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: The image of a star is projected onto a planetarium wall by [#permalink] New post   29 Sep 2020, 22:04
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we need to find BC from the figure (here P-projector
W-wall)
from triangle PBC
tan30=(4/AB)
AB=4√3

from triangle AWC
tan30=(16/AC)
AC=16√3

now BC=AC-AB=16√3-4√3=12√3

option B is correct
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Re: The image of a star is projected onto a planetarium wall by [#permalink] New post   13 Jul 2022, 20:31
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The image of a star is projected onto a planetarium wall by [#permalink]
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